LMFDB - Embedded newform 115.2.j.a.104.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [115,2,Mod(4,115)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(115, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([11, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("115.4"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.j (of order $22$, degree $10$, 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:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$10$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			104.1
Character	$\chi$	$=$	115.104
Dual form			115.2.j.a.94.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.44090 - 2.24208i) q^{2} +(-0.487872 - 0.0701454i) q^{3} +(-2.11990 + 4.64194i) q^{4} +(-0.228158 + 2.22440i) q^{5} +(0.545702 + 1.19492i) q^{6} +(-3.20949 + 2.78104i) q^{7} +(8.18609 - 1.17698i) q^{8} +(-2.64538 - 0.776754i) q^{9} +(5.31603 - 2.69358i) q^{10} +(0.178234 + 0.114544i) q^{11} +(1.35985 - 2.11597i) q^{12} +(-2.39517 - 2.07543i) q^{13} +(10.8599 + 3.18874i) q^{14} +(0.267343 - 1.06922i) q^{15} +(-7.75056 - 8.94462i) q^{16} +(2.27327 - 1.03817i) q^{17} +(2.07018 + 7.05037i) q^{18} +(-1.32070 + 2.89192i) q^{19} +(-9.84186 - 5.77460i) q^{20} +(1.76090 - 1.13166i) q^{21} -0.564661i q^{22} +(0.287163 + 4.78723i) q^{23} -4.07633 q^{24} +(-4.89589 - 1.01503i) q^{25} +(-1.20208 + 8.36064i) q^{26} +(2.58116 + 1.17878i) q^{27} +(-6.10561 - 20.7938i) q^{28} +(-1.49565 - 3.27502i) q^{29} +(-2.78248 + 0.941227i) q^{30} +(0.650832 + 4.52664i) q^{31} +(-4.22679 + 14.3951i) q^{32} +(-0.0789206 - 0.0683851i) q^{33} +(-5.60320 - 3.60096i) q^{34} +(-5.45387 - 7.77370i) q^{35} +(9.21360 - 10.6331i) q^{36} +(-1.16326 + 3.96169i) q^{37} +(8.38691 - 1.20586i) q^{38} +(1.02296 + 1.18055i) q^{39} +(0.750358 + 18.4777i) q^{40} +(5.91454 - 1.73666i) q^{41} +(-5.07454 - 2.31747i) q^{42} +(2.10635 + 0.302848i) q^{43} +(-0.909546 + 0.584530i) q^{44} +(2.33137 - 5.70715i) q^{45} +(10.3196 - 7.54174i) q^{46} -1.53180i q^{47} +(3.15386 + 4.90750i) q^{48} +(1.57045 - 10.9227i) q^{49} +(4.77870 + 12.4395i) q^{50} +(-1.18189 + 0.347034i) q^{51} +(14.7116 - 6.71854i) q^{52} +(-0.0963732 + 0.0835079i) q^{53} +(-1.07628 - 7.48567i) q^{54} +(-0.295457 + 0.370329i) q^{55} +(-23.0000 + 26.5434i) q^{56} +(0.847186 - 1.31825i) q^{57} +(-5.18778 + 8.07234i) q^{58} +(-4.84764 + 5.59448i) q^{59} +(4.39650 + 3.50763i) q^{60} +(1.16941 + 8.13341i) q^{61} +(9.21130 - 7.98164i) q^{62} +(10.6505 - 4.86392i) q^{63} +(15.6533 - 4.59622i) q^{64} +(5.16305 - 4.85429i) q^{65} +(-0.0396083 + 0.275482i) q^{66} +(1.24480 + 1.93695i) q^{67} +12.7532i q^{68} +(0.195703 - 2.35570i) q^{69} +(-9.57078 + 23.4291i) q^{70} +(-8.39602 + 5.39579i) q^{71} +(-22.5696 - 3.24501i) q^{72} +(-9.41485 - 4.29962i) q^{73} +(10.5585 - 3.10027i) q^{74} +(2.31737 + 0.838627i) q^{75} +(-10.6244 - 12.2612i) q^{76} +(-0.890591 + 0.128048i) q^{77} +(1.17292 - 3.99460i) q^{78} +(0.218701 - 0.252395i) q^{79} +(21.6647 - 15.1995i) q^{80} +(5.78157 + 3.71559i) q^{81} +(-12.4160 - 10.7585i) q^{82} +(2.63066 - 8.95919i) q^{83} +(1.52017 + 10.5730i) q^{84} +(1.79063 + 5.29352i) q^{85} +(-2.35603 - 5.15898i) q^{86} +(0.499959 + 1.70271i) q^{87} +(1.59386 + 0.727890i) q^{88} +(1.94546 - 13.5310i) q^{89} +(-16.1552 + 2.99630i) q^{90} +13.4591 q^{91} +(-22.8308 - 8.81547i) q^{92} -2.25407i q^{93} +(-3.43441 + 2.20716i) q^{94} +(-6.13146 - 3.59757i) q^{95} +(3.07188 - 6.72648i) q^{96} +(3.09654 + 10.5458i) q^{97} +(-26.7524 + 12.2174i) q^{98} +(-0.382524 - 0.441456i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 14 q^{4} - 9 q^{5} - 18 q^{6} - 12 q^{9} - 13 q^{10} - 26 q^{11} - 26 q^{14} - 10 q^{15} - 18 q^{16} - 14 q^{19} + 49 q^{20} - 22 q^{21} - 68 q^{24} + 21 q^{25} - 42 q^{26} - 24 q^{29} + 19 q^{30}+ \cdots - 60 q^{99}+O(q^{100}) $ 100 * q - 14 * q^4 - 9 * q^5 - 18 * q^6 - 12 * q^9 - 13 * q^10 - 26 * q^11 - 26 * q^14 - 10 * q^15 - 18 * q^16 - 14 * q^19 + 49 * q^20 - 22 * q^21 - 68 * q^24 + 21 * q^25 - 42 * q^26 - 24 * q^29 + 19 * q^30 - 12 * q^31 + 8 * q^34 - 37 * q^35 - 10 * q^36 + 14 * q^39 - q^40 + 8 * q^41 + 166 * q^44 - 42 * q^45 - 18 * q^46 + 32 * q^49 - 23 * q^50 - 22 * q^51 + 116 * q^54 + 27 * q^55 - 116 * q^56 + 50 * q^59 + 123 * q^60 - 38 * q^61 + 10 * q^64 + 76 * q^65 - 28 * q^66 + 80 * q^69 + 102 * q^70 - 110 * q^71 + 22 * q^74 + 6 * q^75 + 4 * q^76 + 42 * q^79 + 18 * q^80 + 204 * q^81 + 56 * q^84 - 121 * q^85 + 132 * q^86 - 66 * q^89 - 198 * q^90 + 76 * q^91 - 70 * q^94 - 74 * q^95 + 236 * q^96 - 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$e\left(\frac{10}{11}\right)$

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 $

$2$	−1.44090	−	2.24208i	−1.01887	−	1.58539i	−0.791112	−	0.611671i	$-0.790498\pi$
$2$	−1.44090	−	2.24208i	−1.01887	−	1.58539i	−0.227755	−	0.973718i	$-0.573139\pi$
$3$	−0.487872	−	0.0701454i	−0.281673	−	0.0404985i	3.03875e−5	−	1.00000i	$-0.499990\pi$
$3$	−0.487872	−	0.0701454i	−0.281673	−	0.0404985i	−0.281703	+	0.959502i	$0.590899\pi$
$4$	−2.11990	+	4.64194i	−1.05995	+	2.32097i
$5$	−0.228158	+	2.22440i	−0.102035	+	0.994781i
$5$	−0.228158	+	2.22440i	−0.102035	+	0.994781i
$6$	0.545702	+	1.19492i	0.222782	+	0.487824i
$7$	−3.20949	+	2.78104i	−1.21307	+	1.05113i	−0.215868	+	0.976423i	$0.569258\pi$
$7$	−3.20949	+	2.78104i	−1.21307	+	1.05113i	−0.997205	+	0.0747114i	$0.976196\pi$
$8$	8.18609	−	1.17698i	2.89422	−	0.416126i
$9$	−2.64538	−	0.776754i	−0.881793	−	0.258918i
$10$	5.31603	−	2.69358i	1.68107	−	0.851785i
$11$	0.178234	+	0.114544i	0.0537396	+	0.0345363i	0.567235	−	0.823556i	$-0.308013\pi$
$11$	0.178234	+	0.114544i	0.0537396	+	0.0345363i	−0.513495	+	0.858092i	$0.671650\pi$
$12$	1.35985	−	2.11597i	0.392556	−	0.610829i
$13$	−2.39517	−	2.07543i	−0.664301	−	0.575620i	0.256074	−	0.966657i	$-0.417571\pi$
$13$	−2.39517	−	2.07543i	−0.664301	−	0.575620i	−0.920375	+	0.391037i	$0.872116\pi$
$14$	10.8599	+	3.18874i	2.90242	+	0.852227i
$15$	0.267343	−	1.06922i	0.0690276	−	0.276071i
$16$	−7.75056	−	8.94462i	−1.93764	−	2.23616i
$17$	2.27327	−	1.03817i	0.551349	−	0.251793i	−0.120204	−	0.992749i	$-0.538355\pi$
$17$	2.27327	−	1.03817i	0.551349	−	0.251793i	0.671553	+	0.740956i	$0.265628\pi$
$18$	2.07018	+	7.05037i	0.487945	+	1.66179i
$19$	−1.32070	+	2.89192i	−0.302989	+	0.663453i	−0.998482	−	0.0550800i	$-0.982459\pi$
$19$	−1.32070	+	2.89192i	−0.302989	+	0.663453i	0.695493	+	0.718533i	$0.255186\pi$
$20$	−9.84186	−	5.77460i	−2.20071	−	1.29124i
$21$	1.76090	−	1.13166i	0.384259	−	0.246948i
$22$		−	0.564661i		−	0.120386i
$23$	0.287163	+	4.78723i	0.0598777	+	0.998206i
$23$	0.287163	+	4.78723i	0.0598777	+	0.998206i
$24$	−4.07633			−0.832076
$25$	−4.89589	−	1.01503i	−0.979178	−	0.203005i
$26$	−1.20208	+	8.36064i	−0.235747	+	1.63966i
$27$	2.58116	+	1.17878i	0.496745	+	0.226856i
$28$	−6.10561	−	20.7938i	−1.15385	−	3.92966i
$29$	−1.49565	−	3.27502i	−0.277736	−	0.608157i	0.718434	−	0.695595i	$-0.244859\pi$
$29$	−1.49565	−	3.27502i	−0.277736	−	0.608157i	−0.996170	+	0.0874385i	$0.972132\pi$
$30$	−2.78248	+	0.941227i	−0.508009	+	0.171844i
$31$	0.650832	+	4.52664i	0.116893	+	0.813008i	0.960943	+	0.276745i	$0.0892556\pi$
$31$	0.650832	+	4.52664i	0.116893	+	0.813008i	−0.844051	+	0.536264i	$0.819835\pi$
$32$	−4.22679	+	14.3951i	−0.747197	+	2.54472i
$33$	−0.0789206	−	0.0683851i	−0.0137383	−	0.0119043i
$34$	−5.60320	−	3.60096i	−0.960941	−	0.617560i
$35$	−5.45387	−	7.77370i	−0.921872	−	1.31399i
$36$	9.21360	−	10.6331i	1.53560	−	1.77218i
$37$	−1.16326	+	3.96169i	−0.191238	+	0.651298i	0.806922	+	0.590659i	$0.201132\pi$
$37$	−1.16326	+	3.96169i	−0.191238	+	0.651298i	−0.998160	+	0.0606389i	$0.980686\pi$
$38$	8.38691	−	1.20586i	1.36054	−	0.195616i
$39$	1.02296	+	1.18055i	0.163804	+	0.189040i
$40$	0.750358	+	18.4777i	0.118642	+	2.92157i
$41$	5.91454	−	1.73666i	0.923696	−	0.271222i	0.214901	−	0.976636i	$-0.431057\pi$
$41$	5.91454	−	1.73666i	0.923696	−	0.271222i	0.708795	+	0.705414i	$0.249239\pi$
$42$	−5.07454	−	2.31747i	−0.783019	−	0.357593i
$43$	2.10635	+	0.302848i	0.321216	+	0.0461839i	0.301037	−	0.953613i	$-0.402667\pi$
$43$	2.10635	+	0.302848i	0.321216	+	0.0461839i	0.0201791	+	0.999796i	$0.493576\pi$
$44$	−0.909546	+	0.584530i	−0.137119	+	0.0881211i
$45$	2.33137	−	5.70715i	0.347540	−	0.850772i
$46$	10.3196	−	7.54174i	1.52154	−	1.11197i
$47$		−	1.53180i		−	0.223435i	−0.993740	−	0.111718i	$-0.964365\pi$
$47$		−	1.53180i		−	0.223435i	0.993740	−	0.111718i	$-0.0356352\pi$
$48$	3.15386	+	4.90750i	0.455220	+	0.708336i
$49$	1.57045	−	10.9227i	0.224349	−	1.56038i
$50$	4.77870	+	12.4395i	0.675810	+	1.75921i
$51$	−1.18189	+	0.347034i	−0.165497	+	0.0485944i
$52$	14.7116	−	6.71854i	2.04013	−	0.931694i
$53$	−0.0963732	+	0.0835079i	−0.0132379	+	0.0114707i	−0.661455	−	0.749985i	$-0.730061\pi$
$53$	−0.0963732	+	0.0835079i	−0.0132379	+	0.0114707i	0.648217	+	0.761456i	$0.275515\pi$
$54$	−1.07628	−	7.48567i	−0.146463	−	1.01867i
$55$	−0.295457	+	0.370329i	−0.0398394	+	0.0499352i
$56$	−23.0000	+	26.5434i	−3.07350	+	3.54701i
$57$	0.847186	−	1.31825i	0.112213	−	0.174606i
$58$	−5.18778	+	8.07234i	−0.681189	+	1.05995i
$59$	−4.84764	+	5.59448i	−0.631109	+	0.728339i	−0.977777	−	0.209649i	$-0.932768\pi$
$59$	−4.84764	+	5.59448i	−0.631109	+	0.728339i	0.346667	+	0.937988i	$0.387313\pi$
$60$	4.39650	+	3.50763i	0.567586	+	0.452833i
$61$	1.16941	+	8.13341i	0.149727	+	1.04138i	0.916665	+	0.399655i	$0.130870\pi$
$61$	1.16941	+	8.13341i	0.149727	+	1.04138i	−0.766938	+	0.641721i	$0.778221\pi$
$62$	9.21130	−	7.98164i	1.16984	−	1.01367i
$63$	10.6505	−	4.86392i	1.34184	−	0.612797i
$64$	15.6533	−	4.59622i	1.95666	−	0.574528i
$65$	5.16305	−	4.85429i	0.640398	−	0.602100i
$66$	−0.0396083	+	0.275482i	−0.00487545	+	0.0339095i
$67$	1.24480	+	1.93695i	0.152077	+	0.236636i	0.908930	−	0.416949i	$-0.136901\pi$
$67$	1.24480	+	1.93695i	0.152077	+	0.236636i	−0.756853	+	0.653585i	$0.773264\pi$
$68$			12.7532i			1.54655i
$69$	0.195703	−	2.35570i	0.0235599	−	0.283593i
$70$	−9.57078	+	23.4291i	−1.14393	+	2.80031i
$71$	−8.39602	+	5.39579i	−0.996424	+	0.640363i	−0.933845	−	0.357677i	$-0.883569\pi$
$71$	−8.39602	+	5.39579i	−0.996424	+	0.640363i	−0.0625790	+	0.998040i	$0.519933\pi$
$72$	−22.5696	−	3.24501i	−2.65985	−	0.382428i
$73$	−9.41485	−	4.29962i	−1.10193	−	0.503232i	−0.220419	−	0.975405i	$-0.570743\pi$
$73$	−9.41485	−	4.29962i	−1.10193	−	0.503232i	−0.881506	+	0.472173i	$0.843470\pi$
$74$	10.5585	−	3.10027i	1.22741	−	0.360399i
$75$	2.31737	+	0.838627i	0.267587	+	0.0968363i
$76$	−10.6244	−	12.2612i	−1.21870	−	1.40646i
$77$	−0.890591	+	0.128048i	−0.101492	+	0.0145924i
$78$	1.17292	−	3.99460i	0.132807	−	0.452300i
$79$	0.218701	−	0.252395i	0.0246058	−	0.0283966i	−0.743313	−	0.668943i	$-0.766747\pi$
$79$	0.218701	−	0.252395i	0.0246058	−	0.0283966i	0.767919	+	0.640547i	$0.221292\pi$
$80$	21.6647	−	15.1995i	2.42219	−	1.69936i
$81$	5.78157	+	3.71559i	0.642397	+	0.412843i
$82$	−12.4160	−	10.7585i	−1.37112	−	1.18808i
$83$	2.63066	−	8.95919i	0.288752	−	0.983399i	−0.679553	−	0.733627i	$-0.737826\pi$
$83$	2.63066	−	8.95919i	0.288752	−	0.983399i	0.968305	−	0.249772i	$-0.0803557\pi$
$84$	1.52017	+	10.5730i	0.165864	+	1.15361i
$85$	1.79063	+	5.29352i	0.194222	+	0.574163i
$86$	−2.35603	−	5.15898i	−0.254057	−	0.556307i
$87$	0.499959	+	1.70271i	0.0536013	+	0.182549i
$88$	1.59386	+	0.727890i	0.169906	+	0.0775933i
$89$	1.94546	−	13.5310i	0.206218	−	1.43428i	−0.579134	−	0.815232i	$-0.696609\pi$
$89$	1.94546	−	13.5310i	0.206218	−	1.43428i	0.785353	−	0.619049i	$-0.212482\pi$
$90$	−16.1552	+	2.99630i	−1.70290	+	0.315838i
$91$	13.4591			1.41090
$92$	−22.8308	−	8.81547i	−2.38027	−	0.919076i
$93$		−	2.25407i		−	0.233737i
$94$	−3.43441	+	2.20716i	−0.354232	+	0.227651i
$95$	−6.13146	−	3.59757i	−0.629074	−	0.369103i
$96$	3.07188	−	6.72648i	0.313523	−	0.686519i
$97$	3.09654	+	10.5458i	0.314406	+	1.07077i	0.953438	+	0.301588i	$0.0975165\pi$
$97$	3.09654	+	10.5458i	0.314406	+	1.07077i	−0.639033	+	0.769179i	$0.720665\pi$
$98$	−26.7524	+	12.2174i	−2.70240	+	1.23414i
$99$	−0.382524	−	0.441456i	−0.0384451	−	0.0443680i
$100$	15.0905	−	20.5747i	1.50905	−	2.05747i
$101$	3.84742	+	1.12971i	0.382833	+	0.112410i	0.467486	−	0.884001i	$-0.345160\pi$
$101$	3.84742	+	1.12971i	0.382833	+	0.112410i	−0.0846527	+	0.996411i	$0.526978\pi$
$102$	2.48106	+	2.14985i	0.245661	+	0.212867i
$103$	−5.05176	+	7.86069i	−0.497765	+	0.774537i	−0.995696	−	0.0926796i	$-0.970457\pi$
$103$	−5.05176	+	7.86069i	−0.497765	+	0.774537i	0.497931	+	0.867216i	$0.334093\pi$
$104$	−22.0498	−	14.1706i	−2.16216	−	1.38954i
$105$	2.11550	+	4.17513i	0.206452	+	0.407451i
$106$	0.326095	+	0.0957502i	0.0316732	+	0.00930008i
$107$	−6.09015	+	0.875632i	−0.588757	+	0.0846505i	−0.430254	−	0.902708i	$-0.641576\pi$
$107$	−6.09015	+	0.875632i	−0.588757	+	0.0846505i	−0.158503	+	0.987358i	$0.550667\pi$
$108$	−10.9436	+	9.48272i	−1.05305	+	0.912475i
$109$	7.97724	+	17.4677i	0.764081	+	1.67310i	0.739268	+	0.673411i	$0.235172\pi$
$109$	7.97724	+	17.4677i	0.764081	+	1.67310i	0.0248125	+	0.999692i	$0.492101\pi$
$110$	1.25603	+	0.128832i	0.119758	+	0.0122836i
$111$	0.845414	−	1.85120i	0.0802432	−	0.175708i
$112$	49.7507	+	7.15307i	4.70100	+	0.675902i
$113$	1.90312	+	2.96131i	0.179030	+	0.278576i	0.919157	−	0.393890i	$-0.128871\pi$
$113$	1.90312	+	2.96131i	0.179030	+	0.278576i	−0.740127	+	0.672467i	$0.765235\pi$
$114$	−4.17632			−0.391148
$115$	−10.7142	−	0.453476i	−0.999106	−	0.0422868i
$116$	18.3731			1.70590
$117$	4.72404	+	7.35075i	0.436738	+	0.679577i
$118$	19.5282	+	2.80773i	1.79772	+	0.258473i
$119$	−4.40886	+	9.65405i	−0.404159	+	0.884985i
$120$	0.930044	−	9.06737i	0.0849010	−	0.827734i
$121$	−4.55092	−	9.96512i	−0.413720	−	0.905920i
$122$	16.5508	−	14.3413i	1.49843	−	1.29840i
$123$	−3.00736	+	0.432393i	−0.271164	+	0.0389875i
$124$	−22.3921	−	6.57492i	−2.01087	−	0.590445i
$125$	3.37485	−	10.6588i	0.301856	−	0.953353i
$126$	−26.2516	−	16.8709i	−2.33868	−	1.50298i
$127$	−3.35340	+	5.21800i	−0.297567	+	0.463023i	−0.957554	−	0.288254i	$-0.906925\pi$
$127$	−3.35340	+	5.21800i	−0.297567	+	0.463023i	0.659987	+	0.751277i	$0.270562\pi$
$128$	−10.1831	−	8.82372i	−0.900069	−	0.779914i
$129$	−1.00639	−	0.295502i	−0.0886075	−	0.0260175i
$130$	−18.3231	−	4.58144i	−1.60704	−	0.401819i
$131$	5.22133	+	6.02574i	0.456190	+	0.526471i	0.936519	−	0.350617i	$-0.114028\pi$
$131$	5.22133	+	6.02574i	0.456190	+	0.526471i	−0.480329	+	0.877088i	$0.659483\pi$
$132$	0.484744	−	0.221375i	0.0421915	−	0.0192682i
$133$	−3.80379	−	12.9545i	−0.329830	−	1.12330i
$134$	2.54916	−	5.58188i	0.220214	−	0.482201i
$135$	−3.21098	+	5.47259i	−0.276357	+	0.471005i
$136$	17.3873	−	11.1741i	1.49095	−	0.958175i
$137$			1.10749i			0.0946190i	0.998880	+	0.0473095i	$0.0150647\pi$
$137$			1.10749i			0.0946190i	−0.998880	+	0.0473095i	$0.984935\pi$
$138$	−5.56365	+	2.95553i	−0.473609	+	0.251592i
$139$	12.0005			1.01787			0.508934	−	0.860806i	$-0.330040\pi$
$139$	12.0005			1.01787			0.508934	+	0.860806i	$0.330040\pi$
$140$	47.6467	−	8.83705i	4.02688	−	0.746867i
$141$	−0.107448	+	0.747320i	−0.00904879	+	0.0629357i
$142$	24.1956	+	11.0498i	2.03045	+	0.927275i
$143$	−0.189173	−	0.644264i	−0.0158194	−	0.0538761i
$144$	13.5554	+	29.6822i	1.12962	+	2.47352i
$145$	7.62620	−	2.57971i	0.633321	−	0.214233i
$146$	3.92574	+	27.3042i	0.324897	+	2.25971i
$147$	−1.53235	+	5.21871i	−0.126386	+	0.430432i
$148$	−15.9239	−	13.7982i	−1.30894	−	1.13420i
$149$	12.8746	+	8.27402i	1.05473	+	0.677834i	0.948587	−	0.316517i	$-0.102513\pi$
$149$	12.8746	+	8.27402i	1.05473	+	0.677834i	0.106144	+	0.994351i	$0.466150\pi$
$150$	−1.45882	−	6.40409i	−0.119112	−	0.522892i
$151$	−3.64943	+	4.21167i	−0.296987	+	0.342741i	−0.884557	−	0.466432i	$-0.845539\pi$
$151$	−3.64943	+	4.21167i	−0.296987	+	0.342741i	0.587570	+	0.809173i	$0.300085\pi$
$152$	−7.40761	+	25.2280i	−0.600836	+	2.04626i
$153$	−6.82007	+	0.980578i	−0.551370	+	0.0792750i
$154$	1.57034	+	1.81227i	0.126542	+	0.146037i
$155$	−10.2175	+	0.414923i	−0.820692	+	0.0333275i
$156$	−7.64863	+	2.24584i	−0.612380	+	0.179811i
$157$	−13.7479	−	6.27846i	−1.09720	−	0.501076i	−0.217240	−	0.976118i	$-0.569705\pi$
$157$	−13.7479	−	6.27846i	−1.09720	−	0.501076i	−0.879963	+	0.475043i	$0.842433\pi$
$158$	−0.881015	−	0.126671i	−0.0700898	−	0.0100774i
$159$	0.0528755	−	0.0339810i	0.00419330	−	0.00269487i
$160$	−31.0561	−	12.6864i	−2.45520	−	1.00295i
$161$	−14.2351	−	14.5659i	−1.12188	−	1.14796i
$162$		−	18.3165i		−	1.43908i
$163$	12.3308	+	19.1871i	0.965823	+	1.50285i	0.861155	+	0.508342i	$0.169741\pi$
$163$	12.3308	+	19.1871i	0.965823	+	1.50285i	0.104667	+	0.994507i	$0.466622\pi$
$164$	−4.47675	+	31.1365i	−0.349576	+	2.43135i
$165$	0.170122	−	0.159948i	0.0132440	−	0.0124520i
$166$	−23.8777	+	7.01113i	−1.85327	+	0.544169i
$167$	1.08091	−	0.493637i	0.0836436	−	0.0381988i	−0.373154	−	0.927769i	$-0.621724\pi$
$167$	1.08091	−	0.493637i	0.0836436	−	0.0381988i	0.456798	+	0.889571i	$0.348996\pi$
$168$	13.0829	−	11.3364i	1.00937	−	0.874624i
$169$	−0.420648	−	2.92567i	−0.0323575	−	0.225051i
$170$	9.28838	−	11.6422i	0.712386	−	0.892913i
$171$	5.74006	−	6.62438i	0.438953	−	0.506579i
$172$	−5.87107	+	9.13557i	−0.447665	+	0.696580i
$173$	6.16806	−	9.59769i	0.468949	−	0.729699i	−0.523544	−	0.851998i	$-0.675391\pi$
$173$	6.16806	−	9.59769i	0.468949	−	0.729699i	0.992493	+	0.122300i	$0.0390269\pi$
$174$	3.09721	−	3.57437i	0.234799	−	0.270972i
$175$	18.5361	−	10.3579i	1.40120	−	0.782987i
$176$	−0.356860	−	2.48202i	−0.0268993	−	0.187089i
$177$	2.75746	−	2.38935i	0.207263	−	0.179594i
$178$	−33.1407	+	15.1349i	−2.48400	+	1.13441i
$179$	−23.4105	+	6.87394i	−1.74978	+	0.513782i	−0.990564	−	0.137054i	$-0.956237\pi$
$179$	−23.4105	+	6.87394i	−1.74978	+	0.513782i	−0.759218	+	0.650836i	$0.774418\pi$
$180$	21.5500	+	22.9207i	1.60624	+	1.70841i
$181$	0.312425	−	2.17296i	0.0232224	−	0.161515i	−0.974910	−	0.222598i	$-0.928546\pi$
$181$	0.312425	−	2.17296i	0.0232224	−	0.161515i	0.998133	+	0.0610828i	$0.0194554\pi$
$182$	−19.3932	−	30.1764i	−1.43752	−	2.23682i
$183$		−	4.05009i		−	0.299391i
$184$	7.98523	+	38.8507i	0.588679	+	2.86411i
$185$	−8.54696	−	3.49143i	−0.628385	−	0.256695i
$186$	−5.05381	+	3.24789i	−0.370563	+	0.238147i
$187$	0.524090	+	0.0753528i	0.0383253	+	0.00551034i
$188$	7.11051	+	3.24726i	0.518587	+	0.236831i
$189$	−11.5624	+	3.39504i	−0.841044	+	0.246953i
$190$	0.768765	+	18.9309i	0.0557721	+	1.37339i
$191$	−13.7124	−	15.8249i	−0.992193	−	1.14505i	−0.989423	−	0.145056i	$-0.953664\pi$
$191$	−13.7124	−	15.8249i	−0.992193	−	1.14505i	−0.00276963	−	0.999996i	$-0.500882\pi$
$192$	−7.95921	+	1.14436i	−0.574407	+	0.0825872i
$193$	−2.56965	+	8.75142i	−0.184967	+	0.629941i	0.813839	+	0.581091i	$0.197374\pi$
$193$	−2.56965	+	8.75142i	−0.184967	+	0.629941i	−0.998806	+	0.0488503i	$0.984444\pi$
$194$	19.1828	−	22.1381i	1.37724	−	1.58942i
$195$	−2.85941	+	2.00611i	−0.204767	+	0.143660i
$196$	47.3733	+	30.4450i	3.38381	+	2.17464i
$197$	13.4139	+	11.6232i	0.955698	+	0.828117i	0.985193	−	0.171448i	$-0.0548445\pi$
$197$	13.4139	+	11.6232i	0.955698	+	0.828117i	−0.0294951	+	0.999565i	$0.509390\pi$
$198$	−0.438602	+	1.49374i	−0.0311701	+	0.106156i
$199$	−2.91570	−	20.2792i	−0.206689	−	1.43755i	−0.783865	−	0.620932i	$-0.786754\pi$
$199$	−2.91570	−	20.2792i	−0.206689	−	1.43755i	0.577176	−	0.816620i	$-0.304155\pi$
$200$	−41.2729	−	2.54672i	−2.91843	−	0.180080i
$201$	−0.471435	−	1.03230i	−0.0332525	−	0.0728128i
$202$	−3.01085	−	10.2540i	−0.211843	−	0.721470i
$203$	13.9083	+	6.35169i	0.976168	+	0.445801i
$204$	0.894579	−	6.22194i	0.0626331	−	0.435623i
$205$	2.51359	+	13.5525i	0.175557	+	0.946549i
$206$	24.9033			1.73510
$207$	2.95884	−	12.8871i	0.205654	−	0.895715i
$208$			37.5096i			2.60083i
$209$	−0.566645	+	0.364161i	−0.0391957	+	0.0251895i
$210$	6.31276	−	10.7591i	0.435622	−	0.742445i
$211$	0.526898	−	1.15375i	0.0362732	−	0.0794271i	−0.890628	−	0.454732i	$-0.849735\pi$
$211$	0.526898	−	1.15375i	0.0362732	−	0.0794271i	0.926901	+	0.375305i	$0.122462\pi$
$212$	−0.183337	−	0.624388i	−0.0125916	−	0.0428831i
$213$	4.47467	−	2.04351i	0.306600	−	0.140019i
$214$	10.7385	+	12.3929i	0.734070	+	0.847162i
$215$	−1.15423	+	4.61627i	−0.0787181	+	0.314827i
$216$	22.5170	+	6.61160i	1.53209	+	0.449863i
$217$	−14.6776	−	12.7182i	−0.996381	−	0.863369i
$218$	27.6696	−	43.0548i	1.87402	−	2.91604i
$219$	4.29164	+	2.75807i	0.290002	+	0.186373i
$220$	−1.09271	−	2.15656i	−0.0736702	−	0.145395i
$221$	−7.59952	−	2.23142i	−0.511199	−	0.150102i
$222$	−5.36869	+	0.771901i	−0.360323	+	0.0518066i
$223$	17.4967	−	15.1610i	1.17167	−	1.01526i	0.172124	−	0.985075i	$-0.444937\pi$
$223$	17.4967	−	15.1610i	1.17167	−	1.01526i	0.999544	−	0.0301815i	$-0.00960852\pi$
$224$	−26.4675	−	57.9558i	−1.76844	−	3.87234i
$225$	12.1631	+	6.48803i	0.810871	+	0.432535i
$226$	3.89729	−	8.53388i	0.259244	−	0.567665i
$227$	11.1815	+	1.60766i	0.742143	+	0.106704i	0.503007	−	0.864282i	$-0.332227\pi$
$227$	11.1815	+	1.60766i	0.742143	+	0.106704i	0.239136	+	0.970986i	$0.423136\pi$
$228$	4.32328	+	6.72715i	0.286316	+	0.445516i
$229$	−1.89000			−0.124894			−0.0624472	−	0.998048i	$-0.519891\pi$
$229$	−1.89000			−0.124894			−0.0624472	+	0.998048i	$0.519891\pi$
$230$	14.4213	+	24.6755i	0.950915	+	1.62706i
$231$	0.443477			0.0291786
$232$	−16.0982	−	25.0493i	−1.05690	−	1.64457i
$233$	−24.7259	−	3.55505i	−1.61985	−	0.232899i	−0.728112	−	0.685458i	$-0.759602\pi$
$233$	−24.7259	−	3.55505i	−1.61985	−	0.232899i	−0.891735	+	0.452559i	$0.850511\pi$
$234$	9.67411	−	21.1834i	0.632417	−	1.38480i
$235$	3.40732	+	0.349491i	0.222269	+	0.0227983i
$236$	−15.6927	−	34.3622i	−1.02151	−	2.23679i
$237$	−0.124403	+	0.107795i	−0.00808081	+	0.00700206i
$238$	27.9978	−	4.02548i	1.81483	−	0.260933i
$239$	16.1546	+	4.74341i	1.04495	+	0.306825i	0.758776	−	0.651352i	$-0.225798\pi$
$239$	16.1546	+	4.74341i	1.04495	+	0.306825i	0.286176	+	0.958177i	$0.407616\pi$
$240$	−11.6358	+	5.89575i	−0.751088	+	0.380569i
$241$	−18.1468	−	11.6622i	−1.16894	−	0.751231i	−0.195618	−	0.980680i	$-0.562671\pi$
$241$	−18.1468	−	11.6622i	−1.16894	−	0.751231i	−0.973321	+	0.229449i	$0.926308\pi$
$242$	−15.7852	+	24.5622i	−1.01471	+	1.57892i
$243$	−8.99356	−	7.79296i	−0.576937	−	0.499919i
$244$	−40.2339	−	11.8137i	−2.57571	−	0.756296i
$245$	23.9381	+	5.98539i	1.52935	+	0.382392i
$246$	5.30275	+	6.11970i	0.338091	+	0.390178i
$247$	9.16527	−	4.18564i	0.583172	−	0.266326i
$248$	10.6556	+	36.2895i	0.676628	+	2.30438i
$249$	−1.91187	+	4.18641i	−0.121160	+	0.265303i
$250$	−28.7607	+	7.79156i	−1.81899	+	0.492782i
$251$	−2.79356	+	1.79531i	−0.176328	+	0.113319i	−0.625828	−	0.779961i	$-0.715239\pi$
$251$	−2.79356	+	1.79531i	−0.176328	+	0.113319i	0.449500	+	0.893281i	$0.351602\pi$
$252$			59.7501i			3.76390i
$253$	−0.497166	+	0.886139i	−0.0312565	+	0.0557111i
$254$	16.5311			1.03725
$255$	−0.502284	−	2.70817i	−0.0314543	−	0.169592i
$256$	−0.467174	+	3.24926i	−0.0291984	+	0.203079i
$257$	−5.21415	−	2.38122i	−0.325250	−	0.148537i	0.246097	−	0.969245i	$-0.420852\pi$
$257$	−5.21415	−	2.38122i	−0.325250	−	0.148537i	−0.571347	+	0.820708i	$0.693579\pi$
$258$	0.787561	+	2.68219i	0.0490314	+	0.166986i
$259$	−7.28415	−	15.9501i	−0.452615	−	0.991089i
$260$	11.5882	+	34.2572i	0.718667	+	2.12454i
$261$	1.41268	+	9.82544i	0.0874430	+	0.608179i
$262$	5.98678	−	20.3891i	0.369865	−	1.25964i
$263$	6.53960	+	5.66660i	0.403249	+	0.349417i	0.832750	−	0.553649i	$-0.186765\pi$
$263$	6.53960	+	5.66660i	0.403249	+	0.349417i	−0.429501	+	0.903066i	$0.641310\pi$
$264$	−0.726540	−	0.466919i	−0.0447154	−	0.0287369i
$265$	−0.163766	−	0.233425i	−0.0100601	−	0.0143392i
$266$	−23.5642	+	27.1945i	−1.44481	+	1.66740i
$267$	−1.89827	+	6.46492i	−0.116172	+	0.395647i
$268$	−11.6301	+	1.67215i	−0.710419	+	0.102143i
$269$	12.4573	+	14.3765i	0.759535	+	0.876550i	0.995456	−	0.0952223i	$-0.0303562\pi$
$269$	12.4573	+	14.3765i	0.759535	+	0.876550i	−0.235921	+	0.971772i	$0.575811\pi$
$270$	16.8967	−	0.686156i	1.02830	−	0.0417581i
$271$	−19.2128	+	5.64139i	−1.16710	+	0.342690i	−0.807186	−	0.590297i	$-0.799011\pi$
$271$	−19.2128	+	5.64139i	−1.16710	+	0.342690i	−0.359910	+	0.932987i	$0.617193\pi$
$272$	−26.9051	−	12.2872i	−1.63136	−	0.745019i
$273$	−6.56633	−	0.944096i	−0.397412	−	0.0571393i
$274$	2.48307	−	1.59578i	0.150008	−	0.0964043i
$275$	−0.756348	−	0.741707i	−0.0456095	−	0.0447266i
$276$	10.5201	+	5.90229i	0.633238	+	0.355276i
$277$		−	9.57679i		−	0.575414i	−0.957719	−	0.287707i	$-0.907107\pi$
$277$		−	9.57679i		−	0.575414i	0.957719	−	0.287707i	$-0.0928929\pi$
$278$	−17.2915	−	26.9060i	−1.03707	−	1.61372i
$279$	1.79438	−	12.4802i	0.107427	−	0.747171i
$280$	−53.7954	−	57.2171i	−3.21489	−	3.41938i
$281$	−12.5323	+	3.67982i	−0.747615	+	0.219520i	−0.633280	−	0.773923i	$-0.718292\pi$
$281$	−12.5323	+	3.67982i	−0.747615	+	0.219520i	−0.114335	+	0.993442i	$0.536474\pi$
$282$	1.83037	−	0.835903i	0.108997	−	0.0497773i
$283$	−11.5284	+	9.98938i	−0.685290	+	0.593807i	−0.926332	−	0.376707i	$-0.877056\pi$
$283$	−11.5284	+	9.98938i	−0.685290	+	0.593807i	0.241042	+	0.970515i	$0.422511\pi$
$284$	−7.24821	−	50.4124i	−0.430102	−	2.99143i
$285$	2.73901	+	2.18525i	0.162245	+	0.129443i
$286$	−1.17191	+	1.35246i	−0.0692966	+	0.0799726i
$287$	−14.1529	+	22.0224i	−0.835420	+	1.29994i
$288$	22.3629	−	34.7974i	1.31775	−	2.05045i
$289$	−7.04266	+	8.12767i	−0.414274	+	0.478098i
$290$	−16.7725	−	13.3814i	−0.984913	−	0.785786i
$291$	−0.770971	−	5.36222i	−0.0451951	−	0.314339i
$292$	39.9172	−	34.5884i	2.33598	−	2.02414i
$293$	0.596326	−	0.272333i	0.0348377	−	0.0159098i	−0.397920	−	0.917420i	$-0.630268\pi$
$293$	0.596326	−	0.272333i	0.0348377	−	0.0159098i	0.432758	+	0.901510i	$0.357541\pi$
$294$	13.9087	−	4.08397i	0.811173	−	0.238182i
$295$	−11.3383	−	12.0595i	−0.660142	−	0.702132i
$296$	−4.85969	+	33.7999i	−0.282464	+	1.96458i
$297$	0.325029	+	0.505755i	0.0188601	+	0.0293469i
$298$		−	40.7879i		−	2.36278i
$299$	9.24774	−	12.0622i	0.534810	−	0.697576i
$300$	−8.80546	+	8.97928i	−0.508383	+	0.518419i
$301$	−7.60255	+	4.88586i	−0.438204	+	0.281617i
$302$	14.7014	+	2.11374i	0.845968	+	0.121632i
$303$	−1.79781	−	0.821031i	−0.103281	−	0.0471670i
$304$	36.1033	−	10.6009i	2.07067	−	0.608003i
$305$	−18.3587	+	0.745529i	−1.05122	+	0.0426889i
$306$	12.0255	+	13.8782i	0.687455	+	0.793365i
$307$	−6.02376	+	0.866086i	−0.343794	+	0.0494301i	−0.312049	−	0.950066i	$-0.601015\pi$
$307$	−6.02376	+	0.866086i	−0.343794	+	0.0494301i	−0.0317447	+	0.999496i	$0.510106\pi$
$308$	1.29358	−	4.40552i	0.0737085	−	0.251028i
$309$	3.01600	−	3.48065i	0.171574	−	0.198007i
$310$	15.6527	+	22.3107i	0.889014	+	1.26716i
$311$	−13.9054	−	8.93646i	−0.788503	−	0.506740i	0.0833425	−	0.996521i	$-0.473440\pi$
$311$	−13.9054	−	8.93646i	−0.788503	−	0.506740i	−0.871846	+	0.489781i	$0.837077\pi$
$312$	9.76350	+	8.46012i	0.552749	+	0.478960i
$313$	−3.96995	+	13.5204i	−0.224395	+	0.764219i	0.767927	+	0.640538i	$0.221288\pi$
$313$	−3.96995	+	13.5204i	−0.224395	+	0.764219i	−0.992322	+	0.123682i	$0.960530\pi$
$314$	5.73251	+	39.8705i	0.323504	+	2.25002i
$315$	8.38930	+	24.8007i	0.472684	+	1.39736i
$316$	0.707976	+	1.55025i	0.0398268	+	0.0872084i
$317$	6.82784	+	23.2535i	0.383490	+	1.30605i	0.894730	+	0.446608i	$0.147368\pi$
$317$	6.82784	+	23.2535i	0.383490	+	1.30605i	−0.511240	+	0.859438i	$0.670814\pi$
$318$	−0.152376	−	0.0695879i	−0.00854483	−	0.00390230i
$319$	0.108558	−	0.755038i	0.00607809	−	0.0422740i
$320$	6.65241	+	35.8678i	0.371881	+	2.00507i
$321$	3.03264			0.169265
$322$	−12.1467	+	52.9043i	−0.676907	+	2.94824i
$323$			7.94523i			0.442084i
$324$	−29.5039	+	18.9610i	−1.63911	+	1.05339i
$325$	9.61988	+	12.5922i	0.533615	+	0.698491i
$326$	25.2516	−	55.2932i	1.39856	−	3.06241i
$327$	−2.66659	−	9.08157i	−0.147463	−	0.502212i
$328$	46.3729	−	21.1778i	2.56052	−	1.16935i
$329$	4.25998	+	4.91628i	0.234861	+	0.271043i
$330$	−0.603745	−	0.150958i	−0.0332351	−	0.00830996i
$331$	28.9737	+	8.50743i	1.59254	+	0.467611i	0.953457	−	0.301530i	$-0.0974973\pi$
$331$	28.9737	+	8.50743i	1.59254	+	0.467611i	0.639079	+	0.769141i	$0.279315\pi$
$332$	36.0113	+	31.2040i	1.97638	+	1.71254i
$333$	6.15451	−	9.57661i	0.337265	−	0.524795i
$334$	−2.66426	−	1.71221i	−0.145782	−	0.0936882i
$335$	−4.59255	+	2.32700i	−0.250918	+	0.127138i
$336$	−23.7702	−	6.97957i	−1.29677	−	0.380766i
$337$	34.1839	−	4.91491i	1.86212	−	0.267732i	0.882753	−	0.469837i	$-0.155687\pi$
$337$	34.1839	−	4.91491i	1.86212	−	0.267732i	0.979364	+	0.202105i	$0.0647782\pi$
$338$	−5.95347	+	5.15871i	−0.323826	+	0.280597i
$339$	−0.720755	−	1.57823i	−0.0391461	−	0.0857179i
$340$	−28.3682	−	2.90974i	−1.53848	−	0.157803i
$341$	−0.402499	+	0.881350i	−0.0217965	+	0.0477278i
$342$	−23.1232	−	3.32462i	−1.25036	−	0.179775i
$343$	9.26427	+	14.4155i	0.500223	+	0.778363i
$344$	17.5993			0.948888
$345$	5.19535	+	0.972791i	0.279709	+	0.0523733i
$346$	−30.4063			−1.63465
$347$	−12.0819	−	18.7998i	−0.648592	−	1.00923i	−0.997402	−	0.0720351i	$-0.977051\pi$
$347$	−12.0819	−	18.7998i	−0.648592	−	1.00923i	0.348810	−	0.937193i	$-0.386586\pi$
$348$	−8.96373	−	1.28879i	−0.480506	−	0.0690864i
$349$	−4.04953	+	8.86724i	−0.216767	+	0.474652i	−0.986510	−	0.163701i	$-0.947657\pi$
$349$	−4.04953	+	8.86724i	−0.216767	+	0.474652i	0.769744	+	0.638353i	$0.220384\pi$
$350$	−49.9320	−	26.6347i	−2.66898	−	1.42369i
$351$	−3.73586	−	8.18039i	−0.199405	−	0.436637i
$352$	−2.40223	+	2.08154i	−0.128039	+	0.110947i
$353$	−22.8067	+	3.27911i	−1.21388	+	0.174530i	−0.719361	−	0.694637i	$-0.755565\pi$
$353$	−22.8067	+	3.27911i	−1.21388	+	0.174530i	−0.494520	+	0.869166i	$0.664656\pi$
$354$	−9.33032	−	2.73963i	−0.495901	−	0.145610i
$355$	−10.0868	−	19.9072i	−0.535351	−	1.05656i
$356$	58.6858	+	37.7151i	3.11034	+	1.99890i
$357$	2.82814	−	4.40068i	0.149681	−	0.232909i
$358$	49.1440	+	42.5835i	2.59734	+	2.25061i
$359$	26.1451	+	7.67691i	1.37989	+	0.405172i	0.885730	−	0.464201i	$-0.153658\pi$
$359$	26.1451	+	7.67691i	1.37989	+	0.405172i	0.494158	+	0.869372i	$0.335477\pi$
$360$	12.3676	−	49.4633i	0.651830	−	2.60694i
$361$	5.82338	+	6.72053i	0.306494	+	0.353712i
$362$	−5.32213	+	2.43054i	−0.279725	+	0.127746i
$363$	1.52126	+	5.18093i	0.0798453	+	0.271928i
$364$	−28.5321	+	62.4765i	−1.49549	+	3.27466i
$365$	11.7121	−	19.9614i	0.613041	−	1.04483i
$366$	−9.08062	+	5.83576i	−0.474652	+	0.305040i
$367$		−	23.1457i		−	1.20819i	−0.796910	−	0.604097i	$-0.793534\pi$
$367$		−	23.1457i		−	1.20819i	0.796910	−	0.604097i	$-0.206466\pi$
$368$	40.5943	−	39.6723i	2.11612	−	2.06806i
$369$	−16.9952			−0.884733
$370$	4.48722	+	24.1938i	0.233279	+	1.25777i
$371$	0.0770703	−	0.536035i	0.00400129	−	0.0278296i
$372$	10.4633	+	4.77842i	0.542496	+	0.247750i
$373$	5.06752	+	17.2584i	0.262386	+	0.893606i	0.980307	+	0.197481i	$0.0632760\pi$
$373$	5.06752	+	17.2584i	0.262386	+	0.893606i	−0.717920	+	0.696125i	$0.754906\pi$
$374$	−0.586213	−	1.28363i	−0.0303123	−	0.0663748i
$375$	−2.39416	+	4.96341i	−0.123634	+	0.256309i
$376$	−1.80290	−	12.5394i	−0.0929773	−	0.646671i
$377$	−3.21473	+	10.9484i	−0.165567	+	0.563869i
$378$	24.2722	+	21.0320i	1.24843	+	1.08177i
$379$	−10.2688	−	6.59938i	−0.527475	−	0.338987i	0.249648	−	0.968337i	$-0.419685\pi$
$379$	−10.2688	−	6.59938i	−0.527475	−	0.338987i	−0.777123	+	0.629349i	$0.783321\pi$
$380$	29.6978	−	20.8354i	1.52347	−	1.06883i
$381$	2.00205	−	2.31049i	0.102568	−	0.118370i
$382$	−15.7226	+	53.5463i	−0.804439	+	2.73967i
$383$	−21.4119	+	3.07857i	−1.09410	+	0.157308i	−0.665654	−	0.746260i	$-0.731848\pi$
$383$	−21.4119	+	3.07857i	−1.09410	+	0.157308i	−0.428445	+	0.903568i	$0.640938\pi$
$384$	4.34912	+	5.01915i	0.221940	+	0.256132i
$385$	−0.0816339	−	2.01024i	−0.00416045	−	0.102452i
$386$	23.3240	−	6.84854i	1.18716	−	0.348581i
$387$	−5.33687	−	2.43727i	−0.271288	−	0.123893i
$388$	−55.5175	−	7.98221i	−2.81847	−	0.405235i
$389$	−2.61810	+	1.68255i	−0.132743	+	0.0853086i	−0.605327	−	0.795977i	$-0.706958\pi$
$389$	−2.61810	+	1.68255i	−0.132743	+	0.0853086i	0.472584	+	0.881286i	$0.343321\pi$
$390$	8.61797	+	3.52044i	0.436388	+	0.178264i
$391$	5.62275	+	10.5845i	0.284355	+	0.535283i
$392$		−	91.2625i		−	4.60945i
$393$	−2.12466	−	3.30604i	−0.107175	−	0.166768i
$394$	6.73209	−	46.8227i	0.339158	−	2.35890i
$395$	0.511528	+	0.544064i	0.0257378	+	0.0273748i
$396$	2.86013	−	0.839810i	0.143727	−	0.0422020i
$397$	1.19506	−	0.545763i	0.0599781	−	0.0273911i	−0.385200	−	0.922833i	$-0.625868\pi$
$397$	1.19506	−	0.545763i	0.0599781	−	0.0273911i	0.445178	+	0.895442i	$0.353140\pi$
$398$	−41.2662	+	35.7574i	−2.06849	+	1.79236i
$399$	0.947062	+	6.58696i	0.0474124	+	0.329760i
$400$	28.8669	+	51.6589i	1.44334	+	2.58295i
$401$	11.0420	−	12.7431i	0.551411	−	0.636362i	−0.409800	−	0.912175i	$-0.634402\pi$
$401$	11.0420	−	12.7431i	0.551411	−	0.636362i	0.961211	+	0.275813i	$0.0889471\pi$
$402$	−1.63521	+	2.54443i	−0.0815567	+	0.126905i
$403$	7.83586	−	12.1928i	0.390332	−	0.607368i
$404$	−13.4002	+	15.4647i	−0.666685	+	0.769396i
$405$	−9.58406	+	12.0128i	−0.476236	+	0.596919i
$406$	−5.79937	−	40.3355i	−0.287818	−	2.00182i
$407$	−0.661119	+	0.572863i	−0.0327705	+	0.0283958i
$408$	−9.26659	+	4.23191i	−0.458765	+	0.209511i
$409$	10.5846	−	3.10793i	0.523377	−	0.153677i	−0.00936341	−	0.999956i	$-0.502981\pi$
$409$	10.5846	−	3.10793i	0.523377	−	0.153677i	0.532740	+	0.846279i	$0.321162\pi$
$410$	26.7640	−	25.1634i	1.32178	−	1.24273i
$411$	0.0776852	−	0.540312i	0.00383193	−	0.0266516i
$412$	−25.7796	−	40.1139i	−1.27007	−	1.97627i
$413$		−	31.4369i		−	1.54691i
$414$	−33.1573	+	11.9350i	−1.62959	+	0.586574i
$415$	19.3286	+	7.89573i	0.948803	+	0.387586i
$416$	39.9999	−	25.7064i	1.96116	−	1.26036i
$417$	−5.85470	−	0.841779i	−0.286706	−	0.0412221i
$418$	1.63295	+	0.745745i	0.0798704	+	0.0364756i
$419$	−11.4349	+	3.35760i	−0.558633	+	0.164029i	−0.548847	−	0.835923i	$-0.684933\pi$
$419$	−11.4349	+	3.35760i	−0.558633	+	0.164029i	−0.00978581	+	0.999952i	$0.503115\pi$
$420$	−23.8654	+	0.969148i	−1.16451	+	0.0472896i
$421$	4.80509	+	5.54537i	0.234186	+	0.270265i	0.860663	−	0.509175i	$-0.170049\pi$
$421$	4.80509	+	5.54537i	0.234186	+	0.270265i	−0.626477	+	0.779440i	$0.715504\pi$
$422$	−3.34599	+	0.481081i	−0.162880	+	0.0234187i
$423$	−1.18983	+	4.05218i	−0.0578514	+	0.197024i
$424$	−0.690633	+	0.797033i	−0.0335401	+	0.0387073i
$425$	−12.1834	+	2.77533i	−0.590984	+	0.134623i
$426$	−11.0293	−	7.08808i	−0.534370	−	0.343418i
$427$	−26.3725	−	22.8519i	−1.27626	−	1.10588i
$428$	8.84591	−	30.1264i	0.427583	−	1.45621i
$429$	0.0471000	+	0.327588i	0.00227401	+	0.0158161i
$430$	12.0132	−	4.06368i	0.579327	−	0.195968i
$431$	0.153248	+	0.335566i	0.00738170	+	0.0161637i	0.913287	−	0.407317i	$-0.133536\pi$
$431$	0.153248	+	0.335566i	0.00738170	+	0.0161637i	−0.905905	+	0.423480i	$0.860808\pi$
$432$	−9.46174	−	32.2237i	−0.455228	−	1.55036i
$433$	13.2727	+	6.06145i	0.637847	+	0.291295i	0.707969	−	0.706244i	$-0.249612\pi$
$433$	13.2727	+	6.06145i	0.637847	+	0.291295i	−0.0701222	+	0.997538i	$0.522339\pi$
$434$	−7.36633	+	51.2340i	−0.353595	+	2.45931i
$435$	−3.90156	+	0.723623i	−0.187066	+	0.0346951i
$436$	−97.9951			−4.69311
$437$	−14.2235	−	5.49202i	−0.680404	−	0.262719i
$438$		−	13.5963i		−	0.649657i
$439$	4.92795	−	3.16700i	0.235198	−	0.151153i	−0.417733	−	0.908570i	$-0.637175\pi$
$439$	4.92795	−	3.16700i	0.235198	−	0.151153i	0.652931	+	0.757417i	$0.273539\pi$
$440$	−1.98277	+	3.37930i	−0.0945247	+	0.161102i
$441$	−12.6387	+	27.6748i	−0.601841	+	1.31785i
$442$	5.94710	+	20.2540i	0.282875	+	0.963383i
$443$	23.6511	−	10.8011i	1.12370	−	0.513176i	0.235151	−	0.971959i	$-0.424442\pi$
$443$	23.6511	−	10.8011i	1.12370	−	0.513176i	0.888548	+	0.458783i	$0.151714\pi$
$444$	6.80097	+	7.84873i	0.322760	+	0.372484i
$445$	29.6544	+	7.41467i	1.40575	+	0.351489i
$446$	−59.2032	−	17.3836i	−2.80335	−	0.823139i
$447$	−5.70078	−	4.93976i	−0.269638	−	0.233643i
$448$	−37.4568	+	58.2840i	−1.76967	+	2.75366i
$449$	19.8038	+	12.7271i	0.934599	+	0.600630i	0.916859	−	0.399212i	$-0.130716\pi$
$449$	19.8038	+	12.7271i	0.934599	+	0.600630i	0.0177405	+	0.999843i	$0.494353\pi$
$450$	−2.97904	−	36.6191i	−0.140433	−	1.72624i
$451$	1.25310	+	0.367942i	0.0590060	+	0.0173257i
$452$	−17.7807	+	2.55647i	−0.836332	+	0.120246i
$453$	2.07589	−	1.79877i	0.0975336	−	0.0845134i
$454$	−12.5069	−	27.3863i	−0.586978	−	1.28530i
$455$	−3.07080	+	29.9384i	−0.143961	+	1.40354i
$456$	5.38359	−	11.7884i	0.252110	−	0.552043i
$457$	32.8980	+	4.73002i	1.53890	+	0.221261i	0.858975	−	0.512017i	$-0.171101\pi$
$457$	32.8980	+	4.73002i	1.53890	+	0.221261i	0.679929	+	0.733278i	$0.262011\pi$
$458$	2.72329	+	4.23752i	0.127251	+	0.198006i
$459$	7.09145			0.331001
$460$	24.8181	−	48.7734i	1.15715	−	2.27407i
$461$	23.0958			1.07568			0.537839	−	0.843047i	$-0.319241\pi$
$461$	23.0958			1.07568			0.537839	+	0.843047i	$0.319241\pi$
$462$	−0.639004	−	0.994309i	−0.0297291	−	0.0462595i
$463$	−4.72475	−	0.679316i	−0.219578	−	0.0315705i	0.0316479	−	0.999499i	$-0.489924\pi$
$463$	−4.72475	−	0.679316i	−0.219578	−	0.0315705i	−0.251225	+	0.967929i	$0.580834\pi$
$464$	−17.7017	+	38.7613i	−0.821781	+	1.79945i
$465$	5.01396	+	0.514284i	0.232517	+	0.0238493i
$466$	27.6568	+	60.5598i	1.28117	+	2.80538i
$467$	10.1103	−	8.76066i	0.467851	−	0.405395i	−0.388775	−	0.921333i	$-0.627102\pi$
$467$	10.1103	−	8.76066i	0.467851	−	0.405395i	0.856626	+	0.515937i	$0.172556\pi$
$468$	−44.1363	+	6.34584i	−2.04020	+	0.293337i
$469$	−9.38190	−	2.75477i	−0.433216	−	0.127204i
$470$	−4.12601	−	8.14307i	−0.190319	−	0.375612i
$471$	6.26682	+	4.02744i	0.288760	+	0.185575i
$472$	−33.0986	+	51.5025i	−1.52349	+	2.37059i
$473$	0.340734	+	0.295248i	0.0156670	+	0.0135755i
$474$	0.420937	+	0.123598i	0.0193343	+	0.00567706i
$475$	9.40136	−	12.8180i	0.431364	−	0.588130i
$476$	−35.4672	−	40.9313i	−1.62564	−	1.87608i
$477$	0.319809	−	0.146052i	0.0146430	−	0.00668725i
$478$	−12.6420	−	43.0545i	−0.578230	−	1.96927i
$479$	4.61756	−	10.1110i	0.210982	−	0.461986i	−0.774323	−	0.632790i	$-0.781909\pi$
$479$	4.61756	−	10.1110i	0.210982	−	0.461986i	0.985305	+	0.170805i	$0.0546368\pi$
$480$	14.2615	+	8.36778i	0.650945	+	0.381935i
$481$	11.0084	−	7.07467i	0.501940	−	0.322577i
$482$			57.4907i			2.61863i
$483$	5.92318	+	8.10484i	0.269514	+	0.368783i
$484$	55.9050			2.54114
$485$	−24.1646	+	4.48181i	−1.09726	+	0.203509i
$486$	−4.51365	+	31.3931i	−0.204743	+	1.42402i
$487$	16.8151	+	7.67921i	0.761966	+	0.347978i	0.758206	−	0.652015i	$-0.226076\pi$
$487$	16.8151	+	7.67921i	0.761966	+	0.347978i	0.00375943	+	0.999993i	$0.498803\pi$
$488$	19.1458	+	65.2045i	0.866688	+	2.95167i
$489$	−4.66996	−	10.2258i	−0.211183	−	0.462426i
$490$	−21.0726	−	62.2954i	−0.951963	−	2.81422i
$491$	−2.64498	−	18.3962i	−0.119366	−	0.830209i	−0.958257	−	0.285909i	$-0.907704\pi$
$491$	−2.64498	−	18.3962i	−0.119366	−	0.830209i	0.838891	−	0.544300i	$-0.183205\pi$
$492$	4.36817	−	14.8766i	0.196932	−	0.670689i
$493$	−6.80005	−	5.89228i	−0.306259	−	0.265375i
$494$	−22.5907	−	14.5182i	−1.01641	−	0.653204i
$495$	1.06925	−	0.750164i	0.0480592	−	0.0337174i
$496$	35.4448	−	40.9054i	1.59152	−	1.83671i
$497$	11.9410	−	40.6674i	0.535628	−	1.82418i
$498$	12.1411	−	1.74562i	0.544054	−	0.0782232i
$499$	−0.884612	−	1.02090i	−0.0396007	−	0.0457016i	0.735604	−	0.677412i	$-0.236899\pi$
$499$	−0.884612	−	1.02090i	−0.0396007	−	0.0457016i	−0.775204	+	0.631711i	$0.782353\pi$
$500$	42.3233	+	38.2616i	1.89275	+	1.71111i
$501$	−0.561974	+	0.165010i	−0.0251071	+	0.00737212i
$502$	8.05047	+	3.67652i	0.359310	+	0.164091i
$503$	17.6902	+	2.54347i	0.788768	+	0.113408i	0.524914	−	0.851155i	$-0.324097\pi$
$503$	17.6902	+	2.54347i	0.788768	+	0.113408i	0.263854	+	0.964563i	$0.415006\pi$
$504$	81.4613	−	52.3520i	3.62857	−	2.33194i
$505$	−3.39073	+	8.30045i	−0.150886	+	0.369365i
$506$	2.70316	−	0.162150i	0.120170	−	0.00720844i
$507$			1.45686i			0.0647014i
$508$	−17.1128	−	26.6280i	−0.759256	−	1.18143i
$509$	−3.43087	+	23.8622i	−0.152071	+	1.05767i	0.760671	+	0.649137i	$0.224870\pi$
$509$	−3.43087	+	23.8622i	−0.152071	+	1.05767i	−0.912742	+	0.408537i	$0.866039\pi$
$510$	−5.34818	+	5.02835i	−0.236822	+	0.222659i
$511$	42.1743	−	12.3835i	1.86568	−	0.547813i
$512$	−16.5549	+	7.56036i	−0.731629	+	0.334124i
$513$	−6.81787	+	5.90772i	−0.301016	+	0.260832i
$514$	2.17416	+	15.1216i	0.0958983	+	0.666987i
$515$	−16.3327	−	13.0306i	−0.719705	−	0.574197i
$516$	3.50515	−	4.04516i	0.154306	−	0.178078i
$517$	0.175458	−	0.273018i	0.00771663	−	0.0120073i
$518$	−25.2656	+	39.3140i	−1.11011	+	1.72736i
$519$	−3.68246	+	4.24978i	−0.161642	+	0.186545i
$520$	36.5518	−	45.8145i	1.60290	−	2.00910i
$521$	1.09059	+	7.58521i	0.0477795	+	0.332314i	0.999666	+	0.0258616i	$0.00823293\pi$
$521$	1.09059	+	7.58521i	0.0477795	+	0.332314i	−0.951886	+	0.306452i	$0.900858\pi$
$522$	19.9939	−	17.3248i	0.875108	−	0.758285i
$523$	21.3351	−	9.74340i	0.932917	−	0.426049i	0.109821	−	0.993951i	$-0.464972\pi$
$523$	21.3351	−	9.74340i	0.932917	−	0.426049i	0.823096	+	0.567902i	$0.192245\pi$
$524$	−39.0399	+	11.4631i	−1.70547	+	0.500770i
$525$	−9.76982	+	3.75312i	−0.426390	+	0.163800i
$526$	3.28207	−	22.8273i	0.143105	−	0.995317i
$527$	6.17893	+	9.61460i	0.269158	+	0.418819i
$528$			1.23594i			0.0537873i
$529$	−22.8351	+	2.74943i	−0.992829	+	0.119541i
$530$	−0.287387	+	0.703519i	−0.0124833	+	0.0305589i
$531$	17.1694	−	11.0341i	0.745088	−	0.478839i
$532$	68.1978	+	9.80536i	2.95675	+	0.425116i
$533$	−17.7707	−	8.11559i	−0.769732	−	0.351525i
$534$	17.2301	−	5.05921i	0.745618	−	0.218933i
$535$	−0.558239	−	13.7467i	−0.0241348	−	0.594322i
$536$	12.4698	+	14.3909i	0.538613	+	0.621593i
$537$	11.9035	−	1.71146i	0.513674	−	0.0738551i
$538$	14.2835	−	48.6453i	0.615807	−	2.09725i
$539$	1.53103	−	1.76691i	0.0659463	−	0.0761061i
$540$	−18.5965	−	26.5066i	−0.800264	−	1.14066i
$541$	−15.1501	−	9.73637i	−0.651353	−	0.418599i	0.172807	−	0.984956i	$-0.444716\pi$
$541$	−15.1501	−	9.73637i	−0.651353	−	0.418599i	−0.824160	+	0.566357i	$0.808353\pi$
$542$	40.3321	+	34.9480i	1.73241	+	1.50115i
$543$	−0.304847	+	1.03821i	−0.0130822	+	0.0445540i
$544$	5.33591	+	37.1121i	0.228775	+	1.59117i
$545$	−40.6752	+	13.7592i	−1.74233	+	0.589377i
$546$	7.34466	+	16.0826i	0.314323	+	0.688271i
$547$	−1.27757	−	4.35102i	−0.0546251	−	0.186036i	0.927661	−	0.373424i	$-0.121816\pi$
$547$	−1.27757	−	4.35102i	−0.0546251	−	0.186036i	−0.982286	+	0.187387i	$0.939998\pi$
$548$	−5.14089	−	2.34777i	−0.219608	−	0.100292i
$549$	3.22413	−	22.4243i	0.137602	−	0.957046i
$550$	−0.573145	+	2.76452i	−0.0244390	+	0.117879i
$551$	11.4464			0.487634
$552$	−1.17057	−	19.5143i	−0.0498228	−	0.830583i
$553$			1.41827i			0.0603112i
$554$	−21.4719	+	13.7992i	−0.912255	+	0.586271i
$555$	3.92492	+	2.30290i	0.166603	+	0.0977528i
$556$	−25.4399	+	55.7056i	−1.07889	+	2.36244i
$557$	1.40984	+	4.80146i	0.0597367	+	0.203444i	0.983954	−	0.178423i	$-0.0570994\pi$
$557$	1.40984	+	4.80146i	0.0597367	+	0.203444i	−0.924217	+	0.381867i	$0.875281\pi$
$558$	−30.5672	+	13.9596i	−1.29401	+	0.590955i
$559$	−4.41654	−	5.09696i	−0.186800	−	0.215578i
$560$	−27.2623	+	109.033i	−1.15204	+	4.60750i
$561$	−0.250403	−	0.0735250i	−0.0105720	−	0.00310423i
$562$	26.3082	+	22.7962i	1.10974	+	0.961599i
$563$	4.79167	−	7.45598i	0.201945	−	0.314232i	−0.725479	−	0.688244i	$-0.758382\pi$
$563$	4.79167	−	7.45598i	0.201945	−	0.314232i	0.927424	+	0.374012i	$0.122018\pi$
$564$	−3.24124	−	2.08302i	−0.136481	−	0.0877108i
$565$	−7.02134	+	3.55764i	−0.295390	+	0.149671i
$566$	39.0082	+	11.4538i	1.63964	+	0.481440i
$567$	−28.8891	+	4.15362i	−1.21323	+	0.174436i
$568$	−62.3799	+	54.0524i	−2.61740	+	2.26799i
$569$	−10.5218	−	23.0394i	−0.441095	−	0.965864i	−0.991396	−	0.130897i	$-0.958214\pi$
$569$	−10.5218	−	23.0394i	−0.441095	−	0.965864i	0.550301	−	0.834967i	$-0.314513\pi$
$570$	0.952859	−	9.28980i	0.0399109	−	0.389107i
$571$	−8.76591	+	19.1947i	−0.366842	+	0.803272i	0.632740	+	0.774364i	$0.281930\pi$
$571$	−8.76591	+	19.1947i	−0.366842	+	0.803272i	−0.999582	+	0.0289077i	$0.990797\pi$
$572$	3.39167	+	0.487648i	0.141813	+	0.0203896i
$573$	5.57984	+	8.68240i	0.233101	+	0.362713i
$574$	69.7688			2.91209
$575$	3.45324	−	23.7292i	0.144010	−	0.989576i
$576$	−44.9791			−1.87413
$577$	−5.39539	−	8.39538i	−0.224613	−	0.349504i	0.710596	−	0.703600i	$-0.248425\pi$
$577$	−5.39539	−	8.39538i	−0.224613	−	0.349504i	−0.935209	+	0.354095i	$0.884789\pi$
$578$	28.3706	+	4.07908i	1.18006	+	0.169667i
$579$	1.86753	−	4.08932i	0.0776120	−	0.169947i
$580$	−4.19196	+	40.8691i	−0.174062	+	1.69700i
$581$	16.4728	+	36.0704i	0.683407	+	1.49645i
$582$	−10.9116	+	9.45499i	−0.452302	+	0.391922i
$583$	−0.0267423	+	0.00384496i	−0.00110755	+	0.000159242i
$584$	−82.1315	−	24.1160i	−3.39862	−	0.997926i
$585$	−17.4288	+	8.83102i	−0.720593	+	0.365118i
$586$	−1.46983	−	0.944606i	−0.0607183	−	0.0390213i
$587$	12.7667	−	19.8653i	0.526937	−	0.819930i	−0.471131	−	0.882063i	$-0.656154\pi$
$587$	12.7667	−	19.8653i	0.526937	−	0.819930i	0.998068	+	0.0621336i	$0.0197905\pi$
$588$	−20.9765	−	18.1763i	−0.865057	−	0.749577i
$589$	−13.9502	−	4.09616i	−0.574810	−	0.168779i
$590$	−10.7010	+	42.7979i	−0.440554	+	1.76196i
$591$	−5.72893	−	6.61154i	−0.235657	−	0.271963i
$592$	44.4517	−	20.3004i	1.82695	−	0.834342i
$593$	−7.74677	−	26.3831i	−0.318122	−	1.08342i	−0.951005	−	0.309176i	$-0.899947\pi$
$593$	−7.74677	−	26.3831i	−0.318122	−	1.08342i	0.632883	−	0.774247i	$-0.281871\pi$
$594$	0.665609	−	1.45748i	0.0273103	−	0.0598012i
$595$	−20.4685	−	12.0097i	−0.839128	−	0.492349i
$596$	−65.7005	+	42.2232i	−2.69120	+	1.72953i
$597$			10.0982i			0.413290i
$598$	−40.3695	−	3.35375i	−1.65083	−	0.137145i
$599$	−21.9118			−0.895294			−0.447647	−	0.894210i	$-0.647738\pi$
$599$	−21.9118			−0.895294			−0.447647	+	0.894210i	$0.647738\pi$
$600$	19.9572	+	4.13758i	0.814751	+	0.168916i
$601$	2.17989	−	15.1615i	0.0889197	−	0.618450i	−0.895820	−	0.444417i	$-0.853411\pi$
$601$	2.17989	−	15.1615i	0.0889197	−	0.618450i	0.984740	−	0.174033i	$-0.0556800\pi$
$602$	21.9090	+	10.0055i	0.892944	+	0.407794i
$603$	−1.78844	−	6.09086i	−0.0728309	−	0.248039i
$604$	−11.8139	−	25.8688i	−0.480700	−	1.05259i
$605$	23.2047	−	7.84943i	0.943406	−	0.319125i
$606$	0.749638	+	5.21385i	0.0304520	+	0.211798i
$607$	3.21890	−	10.9626i	0.130651	−	0.444957i	−0.868018	−	0.496533i	$-0.834606\pi$
$607$	3.21890	−	10.9626i	0.130651	−	0.444957i	0.998669	+	0.0515757i	$0.0164244\pi$
$608$	−36.0472	−	31.2351i	−1.46191	−	1.26675i
$609$	−6.33990	−	4.07441i	−0.256906	−	0.165103i
$610$	28.1246	+	40.0875i	1.13873	+	1.62310i
$611$	−3.17913	+	3.66891i	−0.128614	+	0.148428i
$612$	9.90611	−	33.7371i	0.400431	−	1.36374i
$613$	−26.1539	+	3.76037i	−1.05635	+	0.151880i	−0.648534	−	0.761186i	$-0.724618\pi$
$613$	−26.1539	+	3.76037i	−1.05635	+	0.151880i	−0.407813	+	0.913065i	$0.633709\pi$
$614$	10.6214	+	12.2578i	0.428647	+	0.494685i
$615$	−0.275662	−	6.78821i	−0.0111158	−	0.273727i
$616$	−7.13975	+	2.09642i	−0.287669	+	0.0844672i
$617$	−23.3039	−	10.6425i	−0.938179	−	0.428452i	−0.113172	−	0.993575i	$-0.536101\pi$
$617$	−23.3039	−	10.6425i	−0.938179	−	0.428452i	−0.825006	+	0.565123i	$0.808829\pi$
$618$	−12.1496	−	1.74686i	−0.488730	−	0.0702688i
$619$	5.00338	−	3.21548i	0.201103	−	0.129241i	−0.436214	−	0.899843i	$-0.643681\pi$
$619$	5.00338	−	3.21548i	0.201103	−	0.129241i	0.637316	+	0.770602i	$0.280044\pi$
$620$	19.7342	−	48.3088i	0.792543	−	1.94013i
$621$	−4.90186	+	12.6951i	−0.196705	+	0.509437i
$622$			44.0535i			1.76639i
$623$	31.3862	+	48.8379i	1.25746	+	1.95665i
$624$	2.63113	−	18.2999i	0.105329	−	0.732582i
$625$	22.9394	+	9.93891i	0.917578	+	0.397556i
$626$	36.0341	−	10.5806i	1.44021	−	0.422885i
$627$	0.301995	−	0.137916i	0.0120605	−	0.00550785i
$628$	58.2885	−	50.5073i	2.32597	−	2.01546i
$629$	1.46850	+	10.2136i	0.0585530	+	0.407245i
$630$	43.5170	−	54.5447i	1.73376	−	2.17311i
$631$	−8.58160	+	9.90370i	−0.341628	+	0.394260i	−0.900401	−	0.435061i	$-0.856727\pi$
$631$	−8.58160	+	9.90370i	−0.341628	+	0.394260i	0.558773	+	0.829321i	$0.311272\pi$
$632$	1.49324	−	2.32353i	0.0593981	−	0.0924252i
$633$	−0.337989	+	0.525921i	−0.0134338	+	0.0209035i
$634$	42.2980	−	48.8144i	1.67987	−	1.93867i
$635$	−10.8418	−	8.64983i	−0.430244	−	0.343258i
$636$	0.0456470	+	0.317482i	0.00181002	+	0.0125890i
$637$	−26.4307	+	22.9024i	−1.04722	+	0.907424i
$638$	−1.84928	+	0.844536i	−0.0732136	+	0.0334355i
$639$	26.4019	−	7.75229i	1.04444	−	0.306676i
$640$	21.9508	−	20.6381i	0.867683	−	0.815793i
$641$	−1.32842	+	9.23939i	−0.0524696	+	0.364934i	0.946623	+	0.322343i	$0.104470\pi$
$641$	−1.32842	+	9.23939i	−0.0524696	+	0.364934i	−0.999093	+	0.0425911i	$0.986439\pi$
$642$	−4.36972	−	6.79941i	−0.172459	−	0.268351i
$643$			50.4948i			1.99132i	0.0930531	+	0.995661i	$0.470337\pi$
$643$			50.4948i			1.99132i	−0.0930531	+	0.995661i	$0.529663\pi$
$644$	97.7914	−	35.2002i	3.85352	−	1.38708i
$645$	0.886929	−	2.17118i	0.0349228	−	0.0854903i
$646$	17.8138	−	11.4483i	0.700876	−	0.450426i
$647$	−39.2123	−	5.63788i	−1.54159	−	0.221648i	−0.681514	−	0.731805i	$-0.738678\pi$
$647$	−39.2123	−	5.63788i	−1.54159	−	0.221648i	−0.860081	+	0.510157i	$0.829587\pi$
$648$	51.7016	+	23.6114i	2.03103	+	0.927541i
$649$	−1.50483	+	0.441857i	−0.0590697	+	0.0173444i
$650$	14.3715	−	39.7126i	0.563697	−	1.55766i
$651$	6.26867	+	7.23443i	0.245688	+	0.283540i
$652$	−115.206	+	16.5641i	−4.51180	+	0.648698i
$653$	−10.3763	+	35.3384i	−0.406055	+	1.38290i	0.462198	+	0.886777i	$0.347061\pi$
$653$	−10.3763	+	35.3384i	−0.406055	+	1.38290i	−0.868254	+	0.496121i	$0.834757\pi$
$654$	−16.5193	+	19.0643i	−0.645957	+	0.745474i
$655$	−14.5949	+	10.2395i	−0.570271	+	0.400091i
$656$	−61.3748	−	39.4432i	−2.39628	−	1.54000i
$657$	21.5661	+	18.6872i	0.841375	+	0.729055i
$658$	4.88450	−	16.6351i	0.190418	−	0.648503i
$659$	4.06770	+	28.2914i	0.158455	+	1.10208i	0.901482	+	0.432817i	$0.142480\pi$
$659$	4.06770	+	28.2914i	0.158455	+	1.10208i	−0.743027	+	0.669261i	$0.766611\pi$
$660$	0.381828	+	1.12877i	0.0148626	+	0.0439374i
$661$	14.6961	+	32.1799i	0.571611	+	1.25165i	0.945935	+	0.324355i	$0.105147\pi$
$661$	14.6961	+	32.1799i	0.571611	+	1.25165i	−0.374325	+	0.927298i	$0.622125\pi$
$662$	−22.6737	−	77.2196i	−0.881239	−	3.00122i
$663$	3.55107	+	1.62172i	0.137912	+	0.0629823i
$664$	10.9900	−	76.4370i	0.426494	−	2.96633i
$665$	29.6838	−	5.50547i	1.15109	−	0.213493i
$666$	−30.3395			−1.17563
$667$	15.2488	−	8.10050i	0.590435	−	0.313652i
$668$			6.06400i			0.234623i
$669$	−9.59965	+	6.16932i	−0.371144	+	0.238520i
$670$	11.8347	+	6.94389i	0.457215	+	0.268266i
$671$	−0.723205	+	1.58360i	−0.0279190	+	0.0611341i
$672$	8.84743	+	30.1316i	0.341297	+	1.16235i
$673$	−13.7823	+	6.29418i	−0.531270	+	0.242623i	−0.662942	−	0.748670i	$-0.730693\pi$
$673$	−13.7823	+	6.29418i	−0.531270	+	0.242623i	0.131673	+	0.991293i	$0.457965\pi$
$674$	−60.2751	−	69.5612i	−2.32171	−	2.67940i
$675$	−11.4406	−	8.39111i	−0.440349	−	0.322974i
$676$	14.4725	+	4.24952i	0.556636	+	0.163443i
$677$	−3.02069	−	2.61744i	−0.116095	−	0.100597i	0.594879	−	0.803815i	$-0.297200\pi$
$677$	−3.02069	−	2.61744i	−0.116095	−	0.100597i	−0.710974	+	0.703219i	$0.751745\pi$
$678$	−2.49999	+	3.89006i	−0.0960116	+	0.149397i
$679$	−39.2667	−	25.2352i	−1.50692	−	0.968436i
$680$	20.8887	+	41.2257i	0.801045	+	1.58093i
$681$	−5.34238	−	1.56866i	−0.204720	−	0.0601113i
$682$	2.55601	−	0.367499i	0.0978749	−	0.0140723i
$683$	17.9062	−	15.5158i	0.685162	−	0.593696i	−0.241135	−	0.970492i	$-0.577520\pi$
$683$	17.9062	−	15.5158i	0.685162	−	0.593696i	0.926296	+	0.376795i	$0.122974\pi$
$684$	18.5816	+	40.6881i	0.710486	+	1.55575i
$685$	−2.46349	−	0.252682i	−0.0941252	−	0.00965447i
$686$	18.9718	−	41.5424i	0.724346	−	1.58610i
$687$	0.922076	+	0.132574i	0.0351794	+	0.00505803i
$688$	−13.6166	−	21.1878i	−0.519127	−	0.807777i
$689$	0.404145			0.0153967
$690$	−5.30490	−	13.0501i	−0.201954	−	0.496808i
$691$	−39.4649			−1.50132			−0.750658	−	0.660690i	$-0.770264\pi$
$691$	−39.4649			−1.50132			−0.750658	+	0.660690i	$0.770264\pi$
$692$	31.4762	+	48.9780i	1.19655	+	1.86186i
$693$	2.45541	+	0.353035i	0.0932735	+	0.0134107i
$694$	−24.7419	+	54.1773i	−0.939191	+	2.05654i
$695$	−2.73800	+	26.6938i	−0.103858	+	1.01256i
$696$	6.09677	+	13.3501i	0.231097	+	0.506033i
$697$	11.6424	−	10.0882i	0.440987	−	0.382118i
$698$	25.7160	−	3.69740i	0.973365	−	0.139949i
$699$	11.8137	+	3.46881i	0.446835	+	0.131203i
$700$	8.78614	+	108.002i	0.332085	+	4.08207i
$701$	22.5983	+	14.5230i	0.853525	+	0.548527i	0.892672	−	0.450706i	$-0.148828\pi$
$701$	22.5983	+	14.5230i	0.853525	+	0.548527i	−0.0391475	+	0.999233i	$0.512464\pi$
$702$	−12.9581	+	20.1632i	−0.489072	+	0.761011i
$703$	−9.92059	−	8.59624i	−0.374162	−	0.324213i
$704$	3.31642	+	0.973789i	0.124992	+	0.0367010i
$705$	−1.63782	−	0.409515i	−0.0616840	−	0.0154232i
$706$	40.2142	+	46.4096i	1.51348	+	1.74665i
$707$	−15.4900	+	7.07406i	−0.582562	+	0.266047i
$708$	5.24568	+	17.8651i	0.197145	+	0.671413i
$709$	19.4498	−	42.5891i	0.730453	−	1.59947i	−0.0681963	−	0.997672i	$-0.521724\pi$
$709$	19.4498	−	42.5891i	0.730453	−	1.59947i	0.798649	−	0.601797i	$-0.205548\pi$
$710$	−30.0995	+	51.2995i	−1.12961	+	1.92524i
$711$	−0.774596	+	0.497803i	−0.0290496	+	0.0186691i
$712$		−	113.056i		−	4.23694i
$713$	−21.4832	+	4.41557i	−0.804550	+	0.165364i
$714$	−13.9417			−0.521756
$715$	1.47626	−	0.273802i	0.0552090	−	0.0102396i
$716$	17.7196	−	123.242i	0.662211	−	4.60578i
$717$	−7.54863	−	3.44734i	−0.281909	−	0.128743i
$718$	−20.4602	−	69.6811i	−0.763568	−	2.60048i
$719$	21.2997	+	46.6398i	0.794344	+	1.73937i	0.663777	+	0.747931i	$0.268953\pi$
$719$	21.2997	+	46.6398i	0.794344	+	1.73937i	0.130567	+	0.991439i	$0.458320\pi$
$720$	−69.1178	+	23.3804i	−2.57587	+	0.871336i
$721$	−5.64732	−	39.2779i	−0.210317	−	1.46279i
$722$	6.67709	−	22.7401i	0.248495	−	0.846298i
$723$	8.03527	+	6.96260i	0.298835	+	0.258942i
$724$	9.42447	+	6.05674i	0.350258	+	0.225097i
$725$	3.99832	+	17.5523i	0.148494	+	0.651875i
$726$	9.42408	−	10.8760i	0.349760	−	0.403645i
$727$	−1.93477	+	6.58921i	−0.0717566	+	0.244380i	−0.987559	−	0.157249i	$-0.949738\pi$
$727$	−1.93477	+	6.58921i	−0.0717566	+	0.244380i	0.915803	+	0.401629i	$0.131556\pi$
$728$	110.178	−	15.8412i	4.08346	−	0.587112i
$729$	−9.66065	−	11.1490i	−0.357802	−	0.412925i
$730$	−61.6310	+	2.50277i	−2.28106	+	0.0926316i
$731$	5.10272	−	1.49829i	0.188731	−	0.0554164i
$732$	18.8003	+	8.58581i	0.694879	+	0.317341i
$733$	26.3096	+	3.78275i	0.971767	+	0.139719i	0.609872	−	0.792500i	$-0.291221\pi$
$733$	26.3096	+	3.78275i	0.971767	+	0.139719i	0.361895	+	0.932219i	$0.382130\pi$
$734$	−51.8944	+	33.3505i	−1.91546	+	1.23099i
$735$	−11.2589	−	4.59925i	−0.415290	−	0.169646i
$736$	−70.1264	−	16.1008i	−2.58489	−	0.593484i
$737$			0.487814i			0.0179689i
$738$	24.4883	+	38.1045i	0.901426	+	1.40265i
$739$	−4.31421	+	30.0060i	−0.158701	+	1.10379i	0.742330	+	0.670034i	$0.233721\pi$
$739$	−4.31421	+	30.0060i	−0.158701	+	1.10379i	−0.901031	+	0.433755i	$0.857188\pi$
$740$	34.3258	−	32.2730i	1.26184	−	1.18638i
$741$	−4.76508	+	1.39915i	−0.175050	+	0.0513992i
$742$	−1.31288	+	0.599574i	−0.0481975	+	0.0220111i
$743$	0.636267	−	0.551328i	0.0233424	−	0.0202263i	−0.643111	−	0.765773i	$-0.722357\pi$
$743$	0.636267	−	0.551328i	0.0233424	−	0.0202263i	0.666454	+	0.745546i	$0.267811\pi$
$744$	−2.65300	−	18.4521i	−0.0972639	−	0.676485i
$745$	−21.3422	+	26.7505i	−0.781916	+	0.980063i
$746$	31.3929	−	36.2293i	1.14938	−	1.32645i
$747$	−13.9182	+	21.6571i	−0.509239	+	0.792391i
$748$	−1.46080	+	2.27306i	−0.0534123	+	0.0831111i
$749$	17.1111	−	19.7473i	0.625227	−	0.721550i
$750$	14.5781	−	1.78385i	0.532317	−	0.0651371i
$751$	5.62454	+	39.1195i	0.205242	+	1.42749i	0.788415	+	0.615144i	$0.210902\pi$
$751$	5.62454	+	39.1195i	0.205242	+	1.42749i	−0.583172	+	0.812348i	$0.698189\pi$
$752$	−13.7013	+	11.8723i	−0.499636	+	0.432937i
$753$	1.48883	−	0.679927i	0.0542561	−	0.0247779i
$754$	29.1792	−	8.56778i	1.06264	−	0.312020i
$755$	−8.53579	−	9.07872i	−0.310649	−	0.330408i
$756$	8.75170	−	60.8694i	0.318296	−	2.21380i
$757$	−8.74756	−	13.6115i	−0.317935	−	0.494717i	0.645098	−	0.764100i	$-0.276817\pi$
$757$	−8.74756	−	13.6115i	−0.317935	−	0.494717i	−0.963033	+	0.269383i	$0.913180\pi$
$758$			32.5326i			1.18164i
$759$	0.304712	−	0.397449i	0.0110603	−	0.0144265i
$760$	−54.4270	−	22.2334i	−1.97427	−	0.806491i
$761$	25.2819	−	16.2477i	0.916468	−	0.588978i	0.00483709	−	0.999988i	$-0.498460\pi$
$761$	25.2819	−	16.2477i	0.916468	−	0.588978i	0.911631	+	0.411010i	$0.134824\pi$
$762$	−8.06505	−	1.15958i	−0.292166	−	0.0420071i
$763$	−74.1812	−	33.8774i	−2.68554	−	1.22645i
$764$	102.527	−	30.1048i	3.70931	−	1.08915i
$765$	−0.625145	−	15.3943i	−0.0226022	−	0.556581i
$766$	37.7548	+	43.5714i	1.36414	+	1.57430i
$767$	23.2219	−	3.33880i	0.838493	−	0.120557i
$768$	0.455842	−	1.55246i	0.0164488	−	0.0560194i
$769$	−16.9454	+	19.5560i	−0.611065	+	0.705207i	−0.973985	−	0.226614i	$-0.927235\pi$
$769$	−16.9454	+	19.5560i	−0.611065	+	0.705207i	0.362920	+	0.931820i	$0.381780\pi$
$770$	−4.38950	+	3.07958i	−0.158187	+	0.110980i
$771$	2.37681	+	1.52748i	0.0855986	+	0.0550109i
$772$	−35.1762	−	30.4803i	−1.26602	−	1.09701i
$773$	0.170000	−	0.578966i	0.00611446	−	0.0208240i	−0.956379	−	0.292128i	$-0.905637\pi$
$773$	0.170000	−	0.578966i	0.00611446	−	0.0208240i	0.962494	+	0.271304i	$0.0874549\pi$
$774$	2.22533	+	15.4775i	0.0799879	+	0.556328i
$775$	1.40825	−	22.8225i	0.0505860	−	0.819810i
$776$	37.7608	+	82.6846i	1.35553	+	2.96820i
$777$	2.43491	+	8.29254i	0.0873519	+	0.297493i
$778$	7.54481	+	3.44560i	0.270495	+	0.123531i
$779$	−2.78901	+	19.3980i	−0.0999267	+	0.695005i
$780$	−3.25055	−	17.5260i	−0.116388	−	0.627531i
$781$	−2.11451			−0.0756632
$782$	15.6296	−	27.8579i	0.558913	−	0.996195i
$783$		−	10.2164i		−	0.365105i
$784$	−109.871	+	70.6099i	−3.92397	+	2.52178i
$785$	17.1025	−	29.1483i	0.610414	−	1.04035i
$786$	−4.35099	+	9.52733i	−0.155195	+	0.339829i
$787$	3.22883	+	10.9964i	0.115095	+	0.391979i	0.996811	−	0.0798032i	$-0.0254292\pi$
$787$	3.22883	+	10.9964i	0.115095	+	0.391979i	−0.881715	+	0.471782i	$0.843611\pi$
$788$	−82.3902	+	37.6264i	−2.93503	+	1.34038i
$789$	−2.79300	−	3.22330i	−0.0994336	−	0.114752i
$790$	0.482776	−	1.93083i	0.0171764	−	0.0686957i
$791$	−14.3435	−	4.21165i	−0.509998	−	0.149749i
$792$	−3.65096	−	3.16358i	−0.129731	−	0.112413i
$793$	14.0794	−	21.9079i	0.499973	−	0.777973i
$794$	−2.94560	−	1.89302i	−0.104535	−	0.0671807i
$795$	0.0635233	+	0.125369i	0.00225294	+	0.00444638i
$796$	100.316	+	29.4554i	3.55560	+	1.04402i
$797$	30.7978	−	4.42805i	1.09091	−	0.156850i	0.426700	−	0.904393i	$-0.359676\pi$
$797$	30.7978	−	4.42805i	1.09091	−	0.156850i	0.664213	+	0.747543i	$0.268767\pi$
$798$	13.4039	−	11.6145i	0.474492	−	0.411149i
$799$	−1.59026	−	3.48219i	−0.0562594	−	0.123191i
$800$	35.3053	−	66.1866i	1.24823	−	2.34005i
$801$	−15.6567	+	34.2834i	−0.553203	+	1.21135i
$802$	−44.4815	−	6.39547i	−1.57070	−	0.225832i
$803$	−1.18555	−	1.84475i	−0.0418372	−	0.0650999i
$804$	5.79127			0.204242
$805$	35.6483	−	28.3412i	1.25644	−	0.998897i
$806$	−38.6280			−1.36061
$807$	−5.06912	−	7.88771i	−0.178442	−	0.277660i
$808$	32.8250	+	4.71953i	1.15478	+	0.166032i
$809$	16.5130	−	36.1583i	0.580565	−	1.27126i	−0.360413	−	0.932793i	$-0.617364\pi$
$809$	16.5130	−	36.1583i	0.580565	−	1.27126i	0.940978	−	0.338467i	$-0.109908\pi$
$810$	40.7432	+	4.17905i	1.43157	+	0.146837i
$811$	−17.7759	−	38.9238i	−0.624196	−	1.36680i	−0.912428	−	0.409238i	$-0.865795\pi$
$811$	−17.7759	−	38.9238i	−0.624196	−	1.36680i	0.288232	−	0.957561i	$-0.406933\pi$
$812$	−58.9683	+	51.0963i	−2.06938	+	1.79313i
$813$	9.76912	−	1.40459i	0.342618	−	0.0492610i
$814$	2.23701	+	0.656845i	0.0784071	+	0.0230224i
$815$	−45.4931	+	23.0509i	−1.59355	+	0.807438i
$816$	12.2644	+	7.88184i	0.429339	+	0.275920i
$817$	−3.65767	+	5.69144i	−0.127966	+	0.199118i
$818$	−22.2196	−	19.2534i	−0.776890	−	0.673179i
$819$	−35.6045	−	10.4544i	−1.24412	−	0.365307i
$820$	−68.2386	−	17.0621i	−2.38299	−	0.595835i
$821$	−25.5160	−	29.4471i	−0.890515	−	1.02771i	−0.999433	−	0.0336587i	$-0.989284\pi$
$821$	−25.5160	−	29.4471i	−0.890515	−	1.02771i	0.108918	−	0.994051i	$-0.465261\pi$
$822$	−1.32336	+	0.604358i	−0.0461574	+	0.0210794i
$823$	−6.84819	−	23.3228i	−0.238713	−	0.812982i	−0.988489	−	0.151291i	$-0.951657\pi$
$823$	−6.84819	−	23.3228i	−0.238713	−	0.812982i	0.749776	−	0.661691i	$-0.230161\pi$
$824$	−32.1023	+	70.2942i	−1.11834	+	2.44881i
$825$	0.316974	+	0.414912i	0.0110356	+	0.0144454i
$826$	−70.4840	+	45.2973i	−2.45245	+	1.57610i
$827$			16.1569i			0.561830i	0.959733	+	0.280915i	$0.0906378\pi$
$827$			16.1569i			0.561830i	−0.959733	+	0.280915i	$0.909362\pi$
$828$	53.5487	+	41.0542i	1.86095	+	1.42673i
$829$	4.40490			0.152988			0.0764942	−	0.997070i	$-0.475627\pi$
$829$	4.40490			0.152988			0.0764942	+	0.997070i	$0.475627\pi$
$830$	−10.1477	−	54.7132i	−0.352230	−	1.89912i
$831$	−0.671768	+	4.67225i	−0.0233034	+	0.162079i
$832$	−47.0315	−	21.4786i	−1.63052	−	0.744635i
$833$	−7.76954	−	26.4606i	−0.269198	−	0.916806i
$834$	6.54868	+	14.3396i	0.226762	+	0.496540i
$835$	0.851426	+	2.51701i	0.0294648	+	0.0871047i
$836$	−0.489180	−	3.40232i	−0.0169186	−	0.117672i
$837$	−3.65600	+	12.4512i	−0.126370	+	0.430376i
$838$	24.0046	+	20.8001i	0.829224	+	0.718527i
$839$	13.6982	+	8.80328i	0.472914	+	0.303923i	0.755302	−	0.655377i	$-0.227490\pi$
$839$	13.6982	+	8.80328i	0.472914	+	0.303923i	−0.282388	+	0.959300i	$0.591127\pi$
$840$	22.2317	+	31.6881i	0.767068	+	1.09334i
$841$	10.5022	−	12.1201i	0.362144	−	0.417936i
$842$	5.50952	−	18.7637i	0.189870	−	0.646639i
$843$	6.37229	−	0.916196i	0.219473	−	0.0315555i
$844$	4.23865	+	4.89166i	0.145900	+	0.168378i
$845$	6.60383	−	0.268174i	0.227178	−	0.00922548i
$846$	10.7997	−	3.17109i	0.371302	−	0.109024i
$847$	42.3195	+	19.3267i	1.45412	+	0.664072i
$848$	1.49389	+	0.214789i	0.0513005	+	0.00737590i
$849$	6.32508	−	4.06488i	0.217076	−	0.139506i
$850$	23.7776	+	23.3173i	0.815565	+	0.799777i
$851$	−19.2995	−	4.43112i	−0.661580	−	0.151897i
$852$			25.1032i			0.860023i
$853$	−5.48822	−	8.53984i	−0.187913	−	0.292399i	0.734496	−	0.678613i	$-0.237419\pi$
$853$	−5.48822	−	8.53984i	−0.187913	−	0.292399i	−0.922409	+	0.386215i	$0.873782\pi$
$854$	−13.2357	+	92.0566i	−0.452918	+	3.15011i
$855$	13.4256	+	14.2796i	0.459146	+	0.488351i
$856$	−48.8240	+	14.3360i	−1.66877	+	0.489995i
$857$	45.4301	−	20.7472i	1.55186	−	0.708712i	0.559134	−	0.829077i	$-0.311134\pi$
$857$	45.4301	−	20.7472i	1.55186	−	0.708712i	0.992730	+	0.120365i	$0.0384065\pi$
$858$	0.666612	−	0.577622i	0.0227578	−	0.0197197i
$859$	6.83092	+	47.5101i	0.233068	+	1.62102i	0.684704	+	0.728821i	$0.259932\pi$
$859$	6.83092	+	47.5101i	0.233068	+	1.62102i	−0.451636	+	0.892202i	$0.649159\pi$
$860$	−18.9816	−	15.1439i	−0.647267	−	0.516404i
$861$	8.44958	−	9.75133i	0.287961	−	0.332325i
$862$	0.531552	−	0.827111i	0.0181047	−	0.0281715i
$863$	−2.02546	+	3.15168i	−0.0689474	+	0.107284i	−0.874015	−	0.485898i	$-0.838492\pi$
$863$	−2.02546	+	3.15168i	−0.0689474	+	0.107284i	0.805068	+	0.593183i	$0.202129\pi$
$864$	−27.8787	+	32.1737i	−0.948451	+	1.09457i
$865$	19.9418	+	15.9100i	0.678041	+	0.540956i
$866$	−5.53438	−	38.4924i	−0.188066	−	1.30803i
$867$	4.00604	−	3.47125i	0.136052	−	0.117890i
$868$	90.1523	−	41.1712i	3.05997	−	1.39744i
$869$	0.0678903	−	0.0199344i	0.00230302	−	0.000676228i
$870$	7.24417	+	7.70494i	0.245600	+	0.261222i
$871$	1.03848	−	7.22281i	0.0351877	−	0.244736i
$872$	85.8616	+	133.603i	2.90764	+	4.52438i
$873$		−	30.3030i		−	1.02560i
$874$	8.18111	+	39.8037i	0.276730	+	1.34638i
$875$	18.8110	+	43.5950i	0.635929	+	1.47378i
$876$	−21.9007	+	14.0747i	−0.739956	+	0.475541i
$877$	−6.27851	−	0.902714i	−0.212010	−	0.0304825i	0.0354912	−	0.999370i	$-0.488700\pi$
$877$	−6.27851	−	0.902714i	−0.212010	−	0.0304825i	−0.247501	+	0.968888i	$0.579610\pi$
$878$	−14.2013	−	6.48553i	−0.479271	−	0.218876i
$879$	−0.310033	+	0.0910340i	−0.0104572	+	0.00307050i
$880$	5.60241	−	0.227508i	0.188857	−	0.00766929i
$881$	−2.25176	−	2.59867i	−0.0758637	−	0.0875514i	0.716549	−	0.697537i	$-0.245721\pi$
$881$	−2.25176	−	2.59867i	−0.0758637	−	0.0875514i	−0.792413	+	0.609986i	$0.791175\pi$
$882$	80.2601	−	11.5397i	2.70250	−	0.388561i
$883$	−4.21299	+	14.3481i	−0.141778	+	0.482852i	−0.999512	−	0.0312420i	$-0.990054\pi$
$883$	−4.21299	+	14.3481i	−0.141778	+	0.482852i	0.857734	+	0.514094i	$0.171872\pi$
$884$	26.4684	−	30.5461i	0.890228	−	1.02738i
$885$	4.68573	+	6.67883i	0.157509	+	0.224506i
$886$	−58.2958	−	37.4644i	−1.95848	−	1.25864i
$887$	−18.4550	−	15.9913i	−0.619657	−	0.536936i	0.287471	−	0.957789i	$-0.407185\pi$
$887$	−18.4550	−	15.9913i	−0.619657	−	0.536936i	−0.907129	+	0.420853i	$0.861731\pi$
$888$	4.74181	−	16.1491i	0.159125	−	0.541929i
$889$	−3.74874	−	26.0731i	−0.125729	−	0.874463i
$890$	−26.1046	−	77.1713i	−0.875030	−	2.58679i
$891$	0.604873	+	1.32449i	0.0202640	+	0.0443720i
$892$	33.2851	+	113.359i	1.11447	+	3.79553i
$893$	4.42984	+	2.02304i	0.148239	+	0.0676984i
$894$	−2.86109	+	19.8993i	−0.0956890	+	0.665532i
$895$	−9.94909	−	53.6426i	−0.332562	−	1.79307i
$896$	57.2217			1.91164
$897$	−5.35782	+	5.23613i	−0.178892	+	0.174829i
$898$		−	62.7401i		−	2.09367i
$899$	13.8514	−	8.90177i	0.461971	−	0.296891i
$900$	−55.9016	+	42.7062i	−1.86339	+	1.42354i
$901$	−0.132387	+	0.289888i	−0.00441046	+	0.00965756i
$902$	−0.980626	−	3.33971i	−0.0326513	−	0.111200i
$903$	4.05179	−	1.85039i	0.134835	−	0.0615772i
$904$	19.0645	+	22.0016i	0.634076	+	0.731763i
$905$	4.76226	+	1.19074i	0.158303	+	0.0395814i
$906$	−7.02411	−	2.06246i	−0.233360	−	0.0685208i
$907$	19.8482	+	17.1986i	0.659049	+	0.571069i	0.918857	−	0.394591i	$-0.129114\pi$
$907$	19.8482	+	17.1986i	0.659049	+	0.571069i	−0.259808	+	0.965660i	$0.583659\pi$
$908$	−31.1664	+	48.4959i	−1.03429	+	1.60939i
$909$	−9.30040	−	5.97700i	−0.308475	−	0.198245i
$910$	71.5491	−	36.2532i	2.37183	−	1.20178i
$911$	6.56134	+	1.92658i	0.217387	+	0.0638306i	0.388612	−	0.921401i	$-0.372954\pi$
$911$	6.56134	+	1.92658i	0.217387	+	0.0638306i	−0.171226	+	0.985232i	$0.554773\pi$
$912$	−18.3574	+	2.63939i	−0.607874	+	0.0873991i
$913$	1.49509	−	1.29551i	0.0494804	−	0.0428750i
$914$	−36.7976	−	80.5754i	−1.21716	−	2.66520i
$915$	9.00901	+	0.924059i	0.297829	+	0.0305484i
$916$	4.00661	−	8.77325i	0.132382	−	0.289876i
$917$	−33.5156	−	4.81882i	−1.10678	−	0.159132i
$918$	−10.2181	−	15.8996i	−0.337246	−	0.524765i
$919$	−28.5127			−0.940547			−0.470274	−	0.882521i	$-0.655845\pi$
$919$	−28.5127			−0.940547			−0.470274	+	0.882521i	$0.655845\pi$
$920$	−88.2413	+	8.89825i	−2.90923	+	0.293366i
$921$	2.99957			0.0988394
$922$	−33.2787	−	51.7826i	−1.09597	−	1.70537i
$923$	31.3085	+	4.50148i	1.03053	+	0.148168i
$924$	−0.940128	+	2.05859i	−0.0309279	+	0.0677227i
$925$	9.71639	−	18.2152i	0.319473	−	0.598914i
$926$	5.28479	+	11.5721i	0.173669	+	0.380282i
$927$	19.4696	−	16.8705i	0.639467	−	0.554101i
$928$	53.4661	−	7.68727i	1.75511	−	0.252347i
$929$	13.3622	+	3.92350i	0.438400	+	0.128726i	0.493482	−	0.869756i	$-0.335724\pi$
$929$	13.3622	+	3.92350i	0.438400	+	0.128726i	−0.0550823	+	0.998482i	$0.517542\pi$
$930$	−6.07153	−	11.9827i	−0.199093	−	0.392929i
$931$	29.5135	+	18.9672i	0.967265	+	0.621624i
$932$	68.9189	−	107.240i	2.25751	−	3.51276i
$933$	6.15721	+	5.33525i	0.201578	+	0.174668i
$934$	−34.2101	−	10.0450i	−1.11939	−	0.328682i
$935$	−0.287190	+	1.14859i	−0.00939210	+	0.0375630i
$936$	47.3232	+	54.6138i	1.54681	+	1.78511i
$937$	−19.3865	+	8.85351i	−0.633329	+	0.289232i	−0.706095	−	0.708117i	$-0.749545\pi$
$937$	−19.3865	+	8.85351i	−0.633329	+	0.289232i	0.0727658	+	0.997349i	$0.476817\pi$
$938$	7.34193	+	25.0043i	0.239722	+	0.816419i
$939$	2.88522	−	6.31776i	0.0941558	−	0.206172i
$940$	−8.84552	+	15.0757i	−0.288509	+	0.491716i
$941$	31.8858	−	20.4917i	1.03945	−	0.668011i	0.0945962	−	0.995516i	$-0.469844\pi$
$941$	31.8858	−	20.4917i	1.03945	−	0.668011i	0.944850	+	0.327504i	$0.106208\pi$
$942$		−	19.8538i		−	0.646872i
$943$	10.0122	+	27.8155i	0.326044	+	0.905798i
$944$	87.6124			2.85154
$945$	−4.91386	−	26.4941i	−0.159848	−	0.861853i
$946$	0.171006	−	1.18937i	0.00555989	−	0.0386699i
$947$	15.2194	+	6.95046i	0.494564	+	0.225860i	0.647052	−	0.762446i	$-0.276001\pi$
$947$	15.2194	+	6.95046i	0.494564	+	0.225860i	−0.152489	+	0.988305i	$0.548729\pi$
$948$	−0.236659	−	0.805985i	−0.00768632	−	0.0261772i
$949$	13.6266	+	29.8382i	0.442339	+	0.968588i
$950$	−42.2853	−	2.60920i	−1.37192	−	0.0846535i
$951$	−1.69999	−	11.8237i	−0.0551259	−	0.383409i
$952$	−24.7287	+	84.2181i	−0.801460	+	2.72952i
$953$	29.9380	+	25.9415i	0.969788	+	0.840326i	0.987194	−	0.159522i	$-0.0509954\pi$
$953$	29.9380	+	25.9415i	0.969788	+	0.840326i	−0.0174063	+	0.999848i	$0.505541\pi$
$954$	−0.788271	−	0.506591i	−0.0255212	−	0.0164015i
$955$	38.3295	−	26.8912i	1.24031	−	0.870179i
$956$	−56.2647	+	64.9330i	−1.81973	+	2.10008i
$957$	−0.105925	+	0.360747i	−0.00342407	+	0.0116613i
$958$	−29.3232	+	4.21604i	−0.947389	+	0.136214i
$959$	−3.07997	−	3.55447i	−0.0994573	−	0.114780i
$960$	−0.729562	−	17.9655i	−0.0235465	−	0.579835i
$961$	9.67740	−	2.84154i	0.312174	−	0.0916626i
$962$	−31.7239	−	14.4878i	−1.02282	−	0.467106i
$963$	16.7909	+	2.41417i	0.541080	+	0.0777955i
$964$	92.6050	−	59.5136i	2.98261	−	1.91680i
$965$	−18.8804	−	7.71262i	−0.607780	−	0.248278i
$966$	9.63701	−	24.9585i	0.310066	−	0.803026i
$967$			10.2968i			0.331123i	0.986199	+	0.165561i	$0.0529436\pi$
$967$			10.2968i			0.331123i	−0.986199	+	0.165561i	$0.947056\pi$
$968$	−48.9830	−	76.2191i	−1.57437	−	2.44977i
$969$	0.557321	−	3.87625i	0.0179037	−	0.124523i
$970$	44.8673	+	47.7211i	1.44060	+	1.53223i
$971$	−40.3269	+	11.8410i	−1.29415	+	0.379997i	−0.855099	−	0.518465i	$-0.826504\pi$
$971$	−40.3269	+	11.8410i	−1.29415	+	0.379997i	−0.439052	+	0.898462i	$0.644685\pi$
$972$	55.2400	−	25.2273i	1.77182	−	0.809165i
$973$	−38.5154	+	33.3738i	−1.23475	+	1.06992i
$974$	−7.01146	−	48.7658i	−0.224662	−	1.56256i
$975$	−3.80998	−	6.81818i	−0.122017	−	0.218357i
$976$	63.6867	−	73.4984i	2.03856	−	2.35263i
$977$	7.85492	−	12.2225i	0.251301	−	0.391032i	−0.692568	−	0.721353i	$-0.743521\pi$
$977$	7.85492	−	12.2225i	0.251301	−	0.391032i	0.943869	+	0.330321i	$0.107157\pi$
$978$	−16.1981	+	25.2047i	−0.517958	+	0.805959i
$979$	1.89664	−	2.18884i	0.0606169	−	0.0699556i
$980$	−78.5303	+	98.4308i	−2.50856	+	3.14426i
$981$	−7.53471	−	52.4051i	−0.240565	−	1.67317i
$982$	−37.4346	+	32.4373i	−1.19459	+	1.03512i
$983$	20.8486	−	9.52124i	0.664967	−	0.303680i	−0.0541870	−	0.998531i	$-0.517257\pi$
$983$	20.8486	−	9.52124i	0.664967	−	0.303680i	0.719154	+	0.694850i	$0.244529\pi$
$984$	−24.1096	+	7.07921i	−0.768585	+	0.225677i
$985$	−28.9150	+	27.1858i	−0.921310	+	0.866213i
$986$	−3.41278	+	23.7364i	−0.108685	+	0.755921i
$987$	−1.73347	−	2.69734i	−0.0551770	−	0.0858571i
$988$			51.4178i			1.63582i
$989$	−0.844934	+	10.1706i	−0.0268673	+	0.323405i
$990$	−3.22261	−	1.31643i	−0.102421	−	0.0418390i
$991$	9.57351	−	6.15252i	0.304113	−	0.195441i	−0.379680	−	0.925118i	$-0.623966\pi$
$991$	9.57351	−	6.15252i	0.304113	−	0.195441i	0.683792	+	0.729677i	$0.260329\pi$
$992$	−67.9124	−	9.76433i	−2.15622	−	0.310018i
$993$	−13.5387	−	6.18291i	−0.429637	−	0.196209i
$994$	−108.385	+	31.8248i	−3.43777	+	1.00942i
$995$	45.7741	−	1.85884i	1.45114	−	0.0589292i
$996$	−15.3801	−	17.7496i	−0.487337	−	0.562417i
$997$	−36.5043	+	5.24853i	−1.15610	+	0.166223i	−0.693577	−	0.720383i	$-0.743966\pi$
$997$	−36.5043	+	5.24853i	−1.15610	+	0.166223i	−0.462527	+	0.886605i	$0.653057\pi$
$998$	−1.01430	+	3.45438i	−0.0321070	+	0.109346i
$999$	−7.67251	+	8.85454i	−0.242747	+	0.280145i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.j.a.104.1	yes	100
5.2	odd	4		575.2.k.g.426.10		100
5.3	odd	4		575.2.k.g.426.1		100
5.4	even	2	inner	115.2.j.a.104.10	yes	100
23.2	even	11	inner	115.2.j.a.94.10	yes	100
115.2	odd	44		575.2.k.g.301.10		100
115.48	odd	44		575.2.k.g.301.1		100
115.94	even	22	inner	115.2.j.a.94.1	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.j.a.94.1	✓	100	115.94	even	22	inner
115.2.j.a.94.10	yes	100	23.2	even	11	inner
115.2.j.a.104.1	yes	100	1.1	even	1	trivial
115.2.j.a.104.10	yes	100	5.4	even	2	inner
575.2.k.g.301.1		100	115.48	odd	44
575.2.k.g.301.10		100	115.2	odd	44
575.2.k.g.426.1		100	5.3	odd	4
575.2.k.g.426.10		100	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.j (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.44090 - 2.24208i) q^{2} +(-0.487872 - 0.0701454i) q^{3} +(-2.11990 + 4.64194i) q^{4} +(-0.228158 + 2.22440i) q^{5} +(0.545702 + 1.19492i) q^{6} +(-3.20949 + 2.78104i) q^{7} +(8.18609 - 1.17698i) q^{8} +(-2.64538 - 0.776754i) q^{9} +(5.31603 - 2.69358i) q^{10} +(0.178234 + 0.114544i) q^{11} +(1.35985 - 2.11597i) q^{12} +(-2.39517 - 2.07543i) q^{13} +(10.8599 + 3.18874i) q^{14} +(0.267343 - 1.06922i) q^{15} +(-7.75056 - 8.94462i) q^{16} +(2.27327 - 1.03817i) q^{17} +(2.07018 + 7.05037i) q^{18} +(-1.32070 + 2.89192i) q^{19} +(-9.84186 - 5.77460i) q^{20} +(1.76090 - 1.13166i) q^{21} -0.564661i q^{22} +(0.287163 + 4.78723i) q^{23} -4.07633 q^{24} +(-4.89589 - 1.01503i) q^{25} +(-1.20208 + 8.36064i) q^{26} +(2.58116 + 1.17878i) q^{27} +(-6.10561 - 20.7938i) q^{28} +(-1.49565 - 3.27502i) q^{29} +(-2.78248 + 0.941227i) q^{30} +(0.650832 + 4.52664i) q^{31} +(-4.22679 + 14.3951i) q^{32} +(-0.0789206 - 0.0683851i) q^{33} +(-5.60320 - 3.60096i) q^{34} +(-5.45387 - 7.77370i) q^{35} +(9.21360 - 10.6331i) q^{36} +(-1.16326 + 3.96169i) q^{37} +(8.38691 - 1.20586i) q^{38} +(1.02296 + 1.18055i) q^{39} +(0.750358 + 18.4777i) q^{40} +(5.91454 - 1.73666i) q^{41} +(-5.07454 - 2.31747i) q^{42} +(2.10635 + 0.302848i) q^{43} +(-0.909546 + 0.584530i) q^{44} +(2.33137 - 5.70715i) q^{45} +(10.3196 - 7.54174i) q^{46} -1.53180i q^{47} +(3.15386 + 4.90750i) q^{48} +(1.57045 - 10.9227i) q^{49} +(4.77870 + 12.4395i) q^{50} +(-1.18189 + 0.347034i) q^{51} +(14.7116 - 6.71854i) q^{52} +(-0.0963732 + 0.0835079i) q^{53} +(-1.07628 - 7.48567i) q^{54} +(-0.295457 + 0.370329i) q^{55} +(-23.0000 + 26.5434i) q^{56} +(0.847186 - 1.31825i) q^{57} +(-5.18778 + 8.07234i) q^{58} +(-4.84764 + 5.59448i) q^{59} +(4.39650 + 3.50763i) q^{60} +(1.16941 + 8.13341i) q^{61} +(9.21130 - 7.98164i) q^{62} +(10.6505 - 4.86392i) q^{63} +(15.6533 - 4.59622i) q^{64} +(5.16305 - 4.85429i) q^{65} +(-0.0396083 + 0.275482i) q^{66} +(1.24480 + 1.93695i) q^{67} +12.7532i q^{68} +(0.195703 - 2.35570i) q^{69} +(-9.57078 + 23.4291i) q^{70} +(-8.39602 + 5.39579i) q^{71} +(-22.5696 - 3.24501i) q^{72} +(-9.41485 - 4.29962i) q^{73} +(10.5585 - 3.10027i) q^{74} +(2.31737 + 0.838627i) q^{75} +(-10.6244 - 12.2612i) q^{76} +(-0.890591 + 0.128048i) q^{77} +(1.17292 - 3.99460i) q^{78} +(0.218701 - 0.252395i) q^{79} +(21.6647 - 15.1995i) q^{80} +(5.78157 + 3.71559i) q^{81} +(-12.4160 - 10.7585i) q^{82} +(2.63066 - 8.95919i) q^{83} +(1.52017 + 10.5730i) q^{84} +(1.79063 + 5.29352i) q^{85} +(-2.35603 - 5.15898i) q^{86} +(0.499959 + 1.70271i) q^{87} +(1.59386 + 0.727890i) q^{88} +(1.94546 - 13.5310i) q^{89} +(-16.1552 + 2.99630i) q^{90} +13.4591 q^{91} +(-22.8308 - 8.81547i) q^{92} -2.25407i q^{93} +(-3.43441 + 2.20716i) q^{94} +(-6.13146 - 3.59757i) q^{95} +(3.07188 - 6.72648i) q^{96} +(3.09654 + 10.5458i) q^{97} +(-26.7524 + 12.2174i) q^{98} +(-0.382524 - 0.441456i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 14 q^{4} - 9 q^{5} - 18 q^{6} - 12 q^{9} - 13 q^{10} - 26 q^{11} - 26 q^{14} - 10 q^{15} - 18 q^{16} - 14 q^{19} + 49 q^{20} - 22 q^{21} - 68 q^{24} + 21 q^{25} - 42 q^{26} - 24 q^{29} + 19 q^{30}+ \cdots - 60 q^{99}+O(q^{100}) \) 100 * q - 14 * q^4 - 9 * q^5 - 18 * q^6 - 12 * q^9 - 13 * q^10 - 26 * q^11 - 26 * q^14 - 10 * q^15 - 18 * q^16 - 14 * q^19 + 49 * q^20 - 22 * q^21 - 68 * q^24 + 21 * q^25 - 42 * q^26 - 24 * q^29 + 19 * q^30 - 12 * q^31 + 8 * q^34 - 37 * q^35 - 10 * q^36 + 14 * q^39 - q^40 + 8 * q^41 + 166 * q^44 - 42 * q^45 - 18 * q^46 + 32 * q^49 - 23 * q^50 - 22 * q^51 + 116 * q^54 + 27 * q^55 - 116 * q^56 + 50 * q^59 + 123 * q^60 - 38 * q^61 + 10 * q^64 + 76 * q^65 - 28 * q^66 + 80 * q^69 + 102 * q^70 - 110 * q^71 + 22 * q^74 + 6 * q^75 + 4 * q^76 + 42 * q^79 + 18 * q^80 + 204 * q^81 + 56 * q^84 - 121 * q^85 + 132 * q^86 - 66 * q^89 - 198 * q^90 + 76 * q^91 - 70 * q^94 - 74 * q^95 + 236 * q^96 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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