LMFDB - Embedded newform 950.2.u.h.499.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(99,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 2]))

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

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

chi := DirichletCharacter("950.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.u (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			499.8
Character	$\chi$	$=$	950.499
Dual form			950.2.u.h.99.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.342020 + 0.939693i) q^{2} +(2.84564 + 0.501764i) q^{3} +(-0.766044 + 0.642788i) q^{4} +(0.501764 + 2.84564i) q^{6} +(3.49580 - 2.01830i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(5.02684 + 1.82962i) q^{9} +O(q^{10})$	\(q+(0.342020 + 0.939693i) q^{2} +(2.84564 + 0.501764i) q^{3} +(-0.766044 + 0.642788i) q^{4} +(0.501764 + 2.84564i) q^{6} +(3.49580 - 2.01830i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(5.02684 + 1.82962i) q^{9} +(2.11161 - 3.65741i) q^{11} +(-2.50242 + 1.44477i) q^{12} +(-5.44192 + 0.959556i) q^{13} +(3.09222 + 2.59468i) q^{14} +(0.173648 - 0.984808i) q^{16} +(-0.523948 - 1.43954i) q^{17} +5.34945i q^{18} +(0.805977 + 4.28374i) q^{19} +(10.9605 - 3.98930i) q^{21} +(4.15905 + 0.733353i) q^{22} +(3.83470 + 4.57002i) q^{23} +(-2.21352 - 1.85736i) q^{24} +(-2.76293 - 4.78554i) q^{26} +(5.87931 + 3.39442i) q^{27} +(-1.38060 + 3.79317i) q^{28} +(-4.97373 - 1.81029i) q^{29} +(-1.35962 - 2.35493i) q^{31} +(0.984808 - 0.173648i) q^{32} +(7.84404 - 9.34816i) q^{33} +(1.17352 - 0.984700i) q^{34} +(-5.02684 + 1.82962i) q^{36} -8.71589i q^{37} +(-3.74974 + 2.22249i) q^{38} -15.9672 q^{39} +(-0.560056 + 3.17623i) q^{41} +(7.49743 + 8.93509i) q^{42} +(-1.46718 + 1.74851i) q^{43} +(0.733353 + 4.15905i) q^{44} +(-2.98287 + 5.16648i) q^{46} +(-3.61462 + 9.93108i) q^{47} +(0.988282 - 2.71528i) q^{48} +(4.64708 - 8.04898i) q^{49} +(-0.768663 - 4.35930i) q^{51} +(3.55196 - 4.23306i) q^{52} +(1.66137 + 1.97995i) q^{53} +(-1.17887 + 6.68570i) q^{54} -4.03660 q^{56} +(0.144099 + 12.5944i) q^{57} -5.29293i q^{58} +(-9.90460 + 3.60498i) q^{59} +(-3.45129 + 2.89597i) q^{61} +(1.74789 - 2.08306i) q^{62} +(21.2656 - 3.74969i) q^{63} +(0.500000 + 0.866025i) q^{64} +(11.4672 + 4.17372i) q^{66} +(-3.76316 + 10.3392i) q^{67} +(1.32668 + 0.765961i) q^{68} +(8.61912 + 14.9288i) q^{69} +(-5.73392 - 4.81133i) q^{71} +(-3.43856 - 4.09792i) q^{72} +(1.94167 + 0.342370i) q^{73} +(8.19026 - 2.98101i) q^{74} +(-3.37095 - 2.76346i) q^{76} -17.0474i q^{77} +(-5.46111 - 15.0043i) q^{78} +(-2.15982 + 12.2490i) q^{79} +(2.73346 + 2.29365i) q^{81} +(-3.17623 + 0.560056i) q^{82} +(3.32355 - 1.91885i) q^{83} +(-5.83197 + 10.1013i) q^{84} +(-2.14487 - 0.780669i) q^{86} +(-13.2451 - 7.64707i) q^{87} +(-3.65741 + 2.11161i) q^{88} +(-1.96650 - 11.1526i) q^{89} +(-17.0872 + 14.3378i) q^{91} +(-5.87510 - 1.03594i) q^{92} +(-2.68737 - 7.38349i) q^{93} -10.5684 q^{94} +2.88954 q^{96} +(4.66803 + 12.8253i) q^{97} +(9.15296 + 1.61391i) q^{98} +(17.3064 - 14.5218i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 12 q^{11} + 30 q^{14} + 30 q^{19} - 36 q^{21} - 18 q^{26} + 24 q^{29} + 18 q^{31} + 18 q^{34} - 132 q^{39} + 36 q^{41} - 6 q^{46} + 54 q^{49} - 6 q^{51} - 54 q^{54} - 12 q^{56} - 72 q^{59} + 24 q^{61} + 24 q^{64} + 96 q^{66} - 42 q^{69} - 78 q^{71} - 36 q^{74} + 12 q^{76} + 84 q^{79} - 72 q^{81} - 18 q^{84} - 78 q^{86} + 72 q^{89} + 24 q^{91} - 24 q^{94} + 12 q^{96} - 102 q^{99}+O(q^{100}) $ 48 * q - 12 * q^11 + 30 * q^14 + 30 * q^19 - 36 * q^21 - 18 * q^26 + 24 * q^29 + 18 * q^31 + 18 * q^34 - 132 * q^39 + 36 * q^41 - 6 * q^46 + 54 * q^49 - 6 * q^51 - 54 * q^54 - 12 * q^56 - 72 * q^59 + 24 * q^61 + 24 * q^64 + 96 * q^66 - 42 * q^69 - 78 * q^71 - 36 * q^74 + 12 * q^76 + 84 * q^79 - 72 * q^81 - 18 * q^84 - 78 * q^86 + 72 * q^89 + 24 * q^91 - 24 * q^94 + 12 * q^96 - 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{8}{9}\right)$

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 $

$2$	0.342020	+	0.939693i	0.241845	+	0.664463i
$2$	0.342020	+	0.939693i	0.241845	+	0.664463i
$3$	2.84564	+	0.501764i	1.64293	+	0.289693i	0.917243	−	0.398328i	$-0.130410\pi$
$3$	2.84564	+	0.501764i	1.64293	+	0.289693i	0.725690	+	0.688022i	$0.241521\pi$
$4$	−0.766044	+	0.642788i	−0.383022	+	0.321394i
$5$		0			0
$5$		0			0
$6$	0.501764	+	2.84564i	0.204844	+	1.16173i
$7$	3.49580	−	2.01830i	1.32129	−	0.762846i	0.337354	−	0.941378i	$-0.390468\pi$
$7$	3.49580	−	2.01830i	1.32129	−	0.762846i	0.983934	+	0.178531i	$0.0571346\pi$
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$	5.02684	+	1.82962i	1.67561	+	0.609873i
$10$		0			0
$11$	2.11161	−	3.65741i	0.636674	−	1.10275i	−0.349484	−	0.936942i	$-0.613643\pi$
$11$	2.11161	−	3.65741i	0.636674	−	1.10275i	0.986158	−	0.165809i	$-0.0530234\pi$
$12$	−2.50242	+	1.44477i	−0.722385	+	0.417069i
$13$	−5.44192	+	0.959556i	−1.50932	+	0.266133i	−0.866224	−	0.499656i	$-0.833460\pi$
$13$	−5.44192	+	0.959556i	−1.50932	+	0.266133i	−0.643092	+	0.765789i	$0.722349\pi$
$14$	3.09222	+	2.59468i	0.826430	+	0.693457i
$15$		0			0
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−0.523948	−	1.43954i	−0.127076	−	0.349139i	0.859797	−	0.510636i	$-0.170590\pi$
$17$	−0.523948	−	1.43954i	−0.127076	−	0.349139i	−0.986873	+	0.161497i	$0.948368\pi$
$18$			5.34945i			1.26088i
$19$	0.805977	+	4.28374i	0.184904	+	0.982757i
$19$	0.805977	+	4.28374i	0.184904	+	0.982757i
$20$		0			0
$21$	10.9605	−	3.98930i	2.39178	−	0.870537i
$22$	4.15905	+	0.733353i	0.886713	+	0.156351i
$23$	3.83470	+	4.57002i	0.799591	+	0.952915i	0.999639	−	0.0268711i	$-0.00855436\pi$
$23$	3.83470	+	4.57002i	0.799591	+	0.952915i	−0.200048	+	0.979786i	$0.564110\pi$
$24$	−2.21352	−	1.85736i	−0.451832	−	0.379132i
$25$		0			0
$26$	−2.76293	−	4.78554i	−0.541856	−	0.938522i
$27$	5.87931	+	3.39442i	1.13147	+	0.653257i
$28$	−1.38060	+	3.79317i	−0.260909	+	0.716841i
$29$	−4.97373	−	1.81029i	−0.923598	−	0.336162i	−0.163929	−	0.986472i	$-0.552417\pi$
$29$	−4.97373	−	1.81029i	−0.923598	−	0.336162i	−0.759669	+	0.650310i	$0.774639\pi$
$30$		0			0
$31$	−1.35962	−	2.35493i	−0.244195	−	0.422958i	0.717710	−	0.696342i	$-0.245190\pi$
$31$	−1.35962	−	2.35493i	−0.244195	−	0.422958i	−0.961905	+	0.273384i	$0.911857\pi$
$32$	0.984808	−	0.173648i	0.174091	−	0.0306970i
$33$	7.84404	−	9.34816i	1.36547	−	1.62731i
$34$	1.17352	−	0.984700i	0.201257	−	0.168875i
$35$		0			0
$36$	−5.02684	+	1.82962i	−0.837807	+	0.304937i
$37$		−	8.71589i		−	1.43288i	−0.697647	−	0.716442i	$-0.745769\pi$
$37$		−	8.71589i		−	1.43288i	0.697647	−	0.716442i	$-0.254231\pi$
$38$	−3.74974	+	2.22249i	−0.608287	+	0.360536i
$39$	−15.9672			−2.55680
$40$		0			0
$41$	−0.560056	+	3.17623i	−0.0874660	+	0.496044i	0.909331	+	0.416073i	$0.136594\pi$
$41$	−0.560056	+	3.17623i	−0.0874660	+	0.496044i	−0.996797	+	0.0799712i	$0.974517\pi$
$42$	7.49743	+	8.93509i	1.15688	+	1.37871i
$43$	−1.46718	+	1.74851i	−0.223743	+	0.266646i	−0.866225	−	0.499655i	$-0.833460\pi$
$43$	−1.46718	+	1.74851i	−0.223743	+	0.266646i	0.642482	+	0.766301i	$0.277905\pi$
$44$	0.733353	+	4.15905i	0.110557	+	0.627001i
$45$		0			0
$46$	−2.98287	+	5.16648i	−0.439800	+	0.761756i
$47$	−3.61462	+	9.93108i	−0.527246	+	1.44860i	0.335053	+	0.942199i	$0.391246\pi$
$47$	−3.61462	+	9.93108i	−0.527246	+	1.44860i	−0.862300	+	0.506398i	$0.830977\pi$
$48$	0.988282	−	2.71528i	0.142646	−	0.391917i
$49$	4.64708	−	8.04898i	0.663869	−	1.14985i
$50$		0			0
$51$	−0.768663	−	4.35930i	−0.107634	−	0.610424i
$52$	3.55196	−	4.23306i	0.492568	−	0.587020i
$53$	1.66137	+	1.97995i	0.228207	+	0.271966i	0.867982	−	0.496596i	$-0.165417\pi$
$53$	1.66137	+	1.97995i	0.228207	+	0.271966i	−0.639775	+	0.768562i	$0.720972\pi$
$54$	−1.17887	+	6.68570i	−0.160424	+	0.909809i
$55$		0			0
$56$	−4.03660			−0.539414
$57$	0.144099	+	12.5944i	0.0190864	+	1.66817i
$58$		−	5.29293i		−	0.694996i
$59$	−9.90460	+	3.60498i	−1.28947	+	0.469328i	−0.893553	−	0.448958i	$-0.851795\pi$
$59$	−9.90460	+	3.60498i	−1.28947	+	0.469328i	−0.395916	+	0.918287i	$0.629573\pi$
$60$		0			0
$61$	−3.45129	+	2.89597i	−0.441892	+	0.370792i	−0.836417	−	0.548094i	$-0.815354\pi$
$61$	−3.45129	+	2.89597i	−0.441892	+	0.370792i	0.394525	+	0.918885i	$0.370909\pi$
$62$	1.74789	−	2.08306i	0.221982	−	0.264548i
$63$	21.2656	−	3.74969i	2.67921	−	0.472417i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$		0			0
$66$	11.4672	+	4.17372i	1.41152	+	0.513750i
$67$	−3.76316	+	10.3392i	−0.459743	+	1.26313i	0.465934	+	0.884819i	$0.345718\pi$
$67$	−3.76316	+	10.3392i	−0.459743	+	1.26313i	−0.925677	+	0.378314i	$0.876504\pi$
$68$	1.32668	+	0.765961i	0.160884	+	0.0928864i
$69$	8.61912	+	14.9288i	1.03762	+	1.79721i
$70$		0			0
$71$	−5.73392	−	4.81133i	−0.680491	−	0.570999i	0.235659	−	0.971836i	$-0.424275\pi$
$71$	−5.73392	−	4.81133i	−0.680491	−	0.570999i	−0.916150	+	0.400836i	$0.868720\pi$
$72$	−3.43856	−	4.09792i	−0.405238	−	0.482944i
$73$	1.94167	+	0.342370i	0.227256	+	0.0400713i	0.286116	−	0.958195i	$-0.407636\pi$
$73$	1.94167	+	0.342370i	0.227256	+	0.0400713i	−0.0588605	+	0.998266i	$0.518747\pi$
$74$	8.19026	−	2.98101i	0.952099	−	0.346536i
$75$		0			0
$76$	−3.37095	−	2.76346i	−0.386674	−	0.316991i
$77$		−	17.0474i		−	1.94274i
$78$	−5.46111	−	15.0043i	−0.618349	−	1.69890i
$79$	−2.15982	+	12.2490i	−0.242999	+	1.37812i	0.582095	+	0.813120i	$0.302233\pi$
$79$	−2.15982	+	12.2490i	−0.242999	+	1.37812i	−0.825094	+	0.564995i	$0.808878\pi$
$80$		0			0
$81$	2.73346	+	2.29365i	0.303718	+	0.254850i
$82$	−3.17623	+	0.560056i	−0.350756	+	0.0618478i
$83$	3.32355	−	1.91885i	0.364807	−	0.210621i	−0.306381	−	0.951909i	$-0.599118\pi$
$83$	3.32355	−	1.91885i	0.364807	−	0.210621i	0.671187	+	0.741288i	$0.265785\pi$
$84$	−5.83197	+	10.1013i	−0.636320	+	1.10214i
$85$		0			0
$86$	−2.14487	−	0.780669i	−0.231287	−	0.0841817i
$87$	−13.2451	−	7.64707i	−1.42003	−	0.819852i
$88$	−3.65741	+	2.11161i	−0.389881	+	0.225098i
$89$	−1.96650	−	11.1526i	−0.208448	−	1.18217i	−0.891921	−	0.452192i	$-0.850642\pi$
$89$	−1.96650	−	11.1526i	−0.208448	−	1.18217i	0.683472	−	0.729976i	$-0.260469\pi$
$90$		0			0
$91$	−17.0872	+	14.3378i	−1.79122	+	1.50301i
$92$	−5.87510	−	1.03594i	−0.612522	−	0.108004i
$93$	−2.68737	−	7.38349i	−0.278667	−	0.765632i
$94$	−10.5684			−1.09005
$95$		0			0
$96$	2.88954			0.294913
$97$	4.66803	+	12.8253i	0.473967	+	1.30221i	0.914540	+	0.404496i	$0.132553\pi$
$97$	4.66803	+	12.8253i	0.473967	+	1.30221i	−0.440573	+	0.897717i	$0.645225\pi$
$98$	9.15296	+	1.61391i	0.924589	+	0.163030i
$99$	17.3064	−	14.5218i	1.73936	−	1.45949i
$100$		0			0
$101$	−2.46911	−	14.0030i	−0.245686	−	1.39335i	−0.818895	−	0.573944i	$-0.805413\pi$
$101$	−2.46911	−	14.0030i	−0.245686	−	1.39335i	0.573209	−	0.819409i	$-0.305698\pi$
$102$	3.83351	−	2.21328i	0.379574	−	0.219147i
$103$	−6.93582	−	4.00440i	−0.683406	−	0.394565i	0.117731	−	0.993046i	$-0.462438\pi$
$103$	−6.93582	−	4.00440i	−0.683406	−	0.394565i	−0.801137	+	0.598481i	$0.795771\pi$
$104$	5.19261	+	1.88996i	0.509178	+	0.185326i
$105$		0			0
$106$	−1.29232	+	2.23836i	−0.125521	+	0.217409i
$107$	15.1979	−	8.77452i	1.46924	−	0.848265i	0.469833	−	0.882755i	$-0.344314\pi$
$107$	15.1979	−	8.77452i	1.46924	−	0.848265i	0.999405	+	0.0344902i	$0.0109807\pi$
$108$	−6.68570	+	1.17887i	−0.643332	+	0.113437i
$109$	−6.11656	−	5.13241i	−0.585861	−	0.491595i	0.301005	−	0.953622i	$-0.402678\pi$
$109$	−6.11656	−	5.13241i	−0.585861	−	0.491595i	−0.886866	+	0.462027i	$0.847122\pi$
$110$		0			0
$111$	4.37332	−	24.8023i	0.415097	−	2.35413i
$112$	−1.38060	−	3.79317i	−0.130454	−	0.358421i
$113$			7.86032i			0.739436i	0.929144	+	0.369718i	$0.120546\pi$
$113$			7.86032i			0.739436i	−0.929144	+	0.369718i	$0.879454\pi$
$114$	−11.7856	+	4.44295i	−1.10382	+	0.416120i
$115$		0			0
$116$	4.97373	−	1.81029i	0.461799	−	0.168081i
$117$	−29.1113	−	5.13310i	−2.69134	−	0.474555i
$118$	−6.77514	−	8.07430i	−0.623703	−	0.743300i
$119$	−4.73703	−	3.97484i	−0.434243	−	0.364373i
$120$		0			0
$121$	−3.41777	−	5.91975i	−0.310706	−	0.538159i
$122$	−3.90174	−	2.25267i	−0.353247	−	0.203947i
$123$	−3.18744	+	8.75741i	−0.287402	+	0.789629i
$124$	2.55525	+	0.930034i	0.229468	+	0.0835195i
$125$		0			0
$126$	10.7968	+	18.7006i	0.961856	+	1.66598i
$127$	18.2700	−	3.22150i	1.62120	−	0.285862i	0.711989	−	0.702190i	$-0.247794\pi$
$127$	18.2700	−	3.22150i	1.62120	−	0.285862i	0.909214	+	0.416328i	$0.136683\pi$
$128$	−0.642788	+	0.766044i	−0.0568149	+	0.0677094i
$129$	−5.05241	+	4.23947i	−0.444840	+	0.373265i
$130$		0			0
$131$	9.22255	−	3.35673i	0.805778	−	0.293279i	0.0938991	−	0.995582i	$-0.470067\pi$
$131$	9.22255	−	3.35673i	0.805778	−	0.293279i	0.711878	+	0.702303i	$0.247845\pi$
$132$			12.2032i			1.06215i
$133$	11.4634	+	13.3484i	0.994003	+	1.15745i
$134$	−11.0027			−0.950492
$135$		0			0
$136$	−0.266015	+	1.50865i	−0.0228106	+	0.129366i
$137$	−2.10023	−	2.50295i	−0.179434	−	0.213842i	0.668829	−	0.743417i	$-0.266796\pi$
$137$	−2.10023	−	2.50295i	−0.179434	−	0.213842i	−0.848263	+	0.529575i	$0.822351\pi$
$138$	−11.0805	+	13.2053i	−0.943237	+	1.12411i
$139$	−0.274807	−	1.55851i	−0.0233089	−	0.132191i	0.970933	−	0.239352i	$-0.0769351\pi$
$139$	−0.274807	−	1.55851i	−0.0233089	−	0.132191i	−0.994242	+	0.107161i	$0.965824\pi$
$140$		0			0
$141$	−15.2690	+	26.4466i	−1.28588	+	2.22721i
$142$	2.56005	−	7.03369i	0.214835	−	0.590254i
$143$	−7.98169	+	21.9295i	−0.667463	+	1.83384i
$144$	2.67473	−	4.63276i	0.222894	−	0.386063i
$145$		0			0
$146$	0.342370	+	1.94167i	0.0283347	+	0.160694i
$147$	17.2626	−	20.5728i	1.42380	−	1.69682i
$148$	5.60247	+	6.67676i	0.460520	+	0.548827i
$149$	2.09553	−	11.8843i	0.171672	−	0.973603i	−0.770242	−	0.637751i	$-0.779865\pi$
$149$	2.09553	−	11.8843i	0.171672	−	0.973603i	0.941915	−	0.335852i	$-0.109024\pi$
$150$		0			0
$151$	4.98455			0.405637			0.202818	−	0.979216i	$-0.434990\pi$
$151$	4.98455			0.405637			0.202818	+	0.979216i	$0.434990\pi$
$152$	1.44387	−	4.11281i	0.117113	−	0.333593i
$153$		−	8.19494i		−	0.662522i
$154$	16.0194	−	5.83057i	1.29088	−	0.469841i
$155$		0			0
$156$	12.2316	−	10.2635i	0.979312	−	0.821740i
$157$	−10.0731	+	12.0046i	−0.803919	+	0.958073i	−0.999745	−	0.0225655i	$-0.992817\pi$
$157$	−10.0731	+	12.0046i	−0.803919	+	0.958073i	0.195827	+	0.980639i	$0.437261\pi$
$158$	−12.2490	+	2.15982i	−0.974475	+	0.171826i
$159$	3.73421	+	6.46783i	0.296142	+	0.512933i
$160$		0			0
$161$	22.6290	+	8.23629i	1.78342	+	0.649111i
$162$	−1.22042	+	3.35309i	−0.0958856	+	0.263444i
$163$	7.28558	+	4.20633i	0.570651	+	0.329465i	0.757409	−	0.652940i	$-0.226465\pi$
$163$	7.28558	+	4.20633i	0.570651	+	0.329465i	−0.186758	+	0.982406i	$0.559798\pi$
$164$	−1.61262	−	2.79313i	−0.125924	−	0.218107i
$165$		0			0
$166$	2.93985	+	2.46683i	0.228177	+	0.191463i
$167$	2.05862	+	2.45336i	0.159300	+	0.189847i	0.839791	−	0.542910i	$-0.182678\pi$
$167$	2.05862	+	2.45336i	0.159300	+	0.189847i	−0.680490	+	0.732757i	$0.738233\pi$
$168$	−11.4867	−	2.02542i	−0.886221	−	0.156265i
$169$	16.4777	−	5.99739i	1.26751	−	0.461338i
$170$		0			0
$171$	−3.78609	+	23.0083i	−0.289530	+	1.75949i
$172$		−	2.28252i		−	0.174041i
$173$	−4.83471	−	13.2833i	−0.367576	−	1.00991i	−0.976280	−	0.216510i	$-0.930533\pi$
$173$	−4.83471	−	13.2833i	−0.367576	−	1.00991i	0.608704	−	0.793397i	$-0.291690\pi$
$174$	2.65580	−	15.0618i	0.201336	−	1.14183i
$175$		0			0
$176$	−3.23517	−	2.71463i	−0.243860	−	0.204623i
$177$	−29.9938	+	5.28872i	−2.25447	+	0.397524i
$178$	9.80739	−	5.66230i	0.735095	−	0.424407i
$179$	8.50106	−	14.7243i	0.635399	−	1.10054i	−0.351031	−	0.936364i	$-0.614169\pi$
$179$	8.50106	−	14.7243i	0.635399	−	1.10054i	0.986430	−	0.164180i	$-0.0524978\pi$
$180$		0			0
$181$	−18.7494	−	6.82423i	−1.39363	−	0.507241i	−0.467352	−	0.884072i	$-0.654792\pi$
$181$	−18.7494	−	6.82423i	−1.39363	−	0.507241i	−0.926282	+	0.376830i	$0.877014\pi$
$182$	−19.3173	−	11.1529i	−1.43190	−	0.826705i
$183$	−11.2742	+	6.50918i	−0.833415	+	0.481172i
$184$	−1.03594	−	5.87510i	−0.0763705	−	0.433118i
$185$		0			0
$186$	6.01908	−	5.05061i	0.441340	−	0.370328i
$187$	−6.37135	−	1.12344i	−0.465919	−	0.0821541i
$188$	−3.61462	−	9.93108i	−0.263623	−	0.724299i
$189$	27.4039			1.99334
$190$		0			0
$191$	10.0735			0.728896			0.364448	−	0.931224i	$-0.381258\pi$
$191$	10.0735			0.728896			0.364448	+	0.931224i	$0.381258\pi$
$192$	0.988282	+	2.71528i	0.0713231	+	0.195959i
$193$	4.53351	+	0.799380i	0.326329	+	0.0575407i	0.334413	−	0.942427i	$-0.391462\pi$
$193$	4.53351	+	0.799380i	0.326329	+	0.0575407i	−0.00808358	+	0.999967i	$0.502573\pi$
$194$	−10.4553	+	8.77303i	−0.750646	+	0.629867i
$195$		0			0
$196$	1.61391	+	9.15296i	0.115280	+	0.653783i
$197$	0.940940	−	0.543252i	0.0670392	−	0.0387051i	−0.466106	−	0.884729i	$-0.654343\pi$
$197$	0.940940	−	0.543252i	0.0670392	−	0.0387051i	0.533145	+	0.846024i	$0.321010\pi$
$198$	19.5651	+	11.2959i	1.39043	+	0.802768i
$199$	−1.22137	−	0.444543i	−0.0865808	−	0.0315128i	0.298367	−	0.954451i	$-0.403558\pi$
$199$	−1.22137	−	0.444543i	−0.0865808	−	0.0315128i	−0.384947	+	0.922939i	$0.625780\pi$
$200$		0			0
$201$	−15.8964	+	27.5334i	−1.12125	+	1.94206i
$202$	12.3141	−	7.10952i	0.866414	−	0.500224i
$203$	−21.0409	+	3.71007i	−1.47678	+	0.260396i
$204$	3.39094	+	2.84533i	0.237413	+	0.199213i
$205$		0			0
$206$	1.39071	−	7.88712i	0.0968955	−	0.549522i
$207$	10.9150	+	29.9888i	0.758647	+	2.08437i
$208$			5.52587i			0.383150i
$209$	17.3693	+	6.09778i	1.20146	+	0.421792i
$210$		0			0
$211$	−4.86776	+	1.77172i	−0.335111	+	0.121970i	−0.504094	−	0.863649i	$-0.668174\pi$
$211$	−4.86776	+	1.77172i	−0.335111	+	0.121970i	0.168984	+	0.985619i	$0.445951\pi$
$212$	−2.54537	−	0.448817i	−0.174817	−	0.0308249i
$213$	−13.9025	−	16.5684i	−0.952586	−	1.13525i
$214$	13.4433	+	11.2803i	0.918968	+	0.771106i
$215$		0			0
$216$	−3.39442	−	5.87931i	−0.230961	−	0.400036i
$217$	−9.50591	−	5.48824i	−0.645303	−	0.372566i
$218$	2.73090	−	7.50308i	0.184960	−	0.508172i
$219$	5.35352	+	1.94852i	0.361758	+	0.131669i
$220$		0			0
$221$	4.23260	+	7.33107i	0.284715	+	0.493141i
$222$	24.8023	−	4.37332i	1.66462	−	0.293518i
$223$	−5.19927	+	6.19625i	−0.348169	+	0.414932i	−0.911500	−	0.411299i	$-0.865075\pi$
$223$	−5.19927	+	6.19625i	−0.348169	+	0.414932i	0.563331	+	0.826231i	$0.309520\pi$
$224$	3.09222	−	2.59468i	0.206607	−	0.173364i
$225$		0			0
$226$	−7.38628	+	2.68839i	−0.491328	+	0.178829i
$227$		−	6.53426i		−	0.433694i	−0.976206	−	0.216847i	$-0.930423\pi$
$227$		−	6.53426i		−	0.433694i	0.976206	−	0.216847i	$-0.0695773\pi$
$228$	−8.20591	−	9.55524i	−0.543450	−	0.632811i
$229$	−25.8896			−1.71084			−0.855418	−	0.517939i	$-0.826699\pi$
$229$	−25.8896			−1.71084			−0.855418	+	0.517939i	$0.826699\pi$
$230$		0			0
$231$	8.55379	−	48.5109i	0.562798	−	3.19179i
$232$	3.40223	+	4.05462i	0.223367	+	0.266199i
$233$	14.5918	−	17.3898i	0.955937	−	1.13924i	−0.0342384	−	0.999414i	$-0.510901\pi$
$233$	14.5918	−	17.3898i	0.955937	−	1.13924i	0.990176	−	0.139828i	$-0.0446550\pi$
$234$	−5.13310	−	29.1113i	−0.335561	−	1.90306i
$235$		0			0
$236$	5.27013	−	9.12813i	0.343056	−	0.594190i
$237$	−12.2922	+	33.7724i	−0.798462	+	2.19376i
$238$	2.11497	−	5.81083i	0.137093	−	0.376660i
$239$	−4.47880	+	7.75751i	−0.289710	+	0.501792i	−0.973740	−	0.227661i	$-0.926892\pi$
$239$	−4.47880	+	7.75751i	−0.289710	+	0.501792i	0.684031	+	0.729453i	$0.260225\pi$
$240$		0			0
$241$	0.582502	+	3.30353i	0.0375223	+	0.212799i	0.997804	−	0.0662321i	$-0.0210978\pi$
$241$	0.582502	+	3.30353i	0.0375223	+	0.212799i	−0.960282	+	0.279031i	$0.909987\pi$
$242$	4.39380	−	5.23633i	0.282444	−	0.336604i
$243$	−6.46376	−	7.70320i	−0.414650	−	0.494161i
$244$	0.782343	−	4.43689i	0.0500844	−	0.284043i
$245$		0			0
$246$	−9.31944			−0.594186
$247$	−8.49655	−	22.5384i	−0.540622	−	1.43408i
$248$			2.71924i			0.172672i
$249$	10.4204	−	3.79273i	0.660369	−	0.240354i
$250$		0			0
$251$	17.0959	−	14.3452i	1.07909	−	0.905460i	0.0832408	−	0.996529i	$-0.473473\pi$
$251$	17.0959	−	14.3452i	1.07909	−	0.905460i	0.995845	+	0.0910693i	$0.0290285\pi$
$252$	−13.8801	+	16.5417i	−0.874365	+	1.04203i
$253$	24.8118	−	4.37499i	1.55991	−	0.275054i
$254$	9.27594	+	16.0664i	0.582024	+	1.00810i
$255$		0			0
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	0.319330	−	0.877351i	0.0199192	−	0.0547277i	−0.929334	−	0.369239i	$-0.879618\pi$
$257$	0.319330	−	0.877351i	0.0199192	−	0.0547277i	0.949254	+	0.314511i	$0.101841\pi$
$258$	−5.71183	−	3.29772i	−0.355603	−	0.205307i
$259$	−17.5913	−	30.4690i	−1.09307	−	1.89325i
$260$		0			0
$261$	−21.6900	−	18.2001i	−1.34258	−	1.12656i
$262$	6.30859	+	7.51829i	0.389746	+	0.464481i
$263$	14.6030	+	2.57491i	0.900462	+	0.158776i	0.604670	−	0.796476i	$-0.293305\pi$
$263$	14.6030	+	2.57491i	0.900462	+	0.158776i	0.295793	+	0.955252i	$0.404416\pi$
$264$	−11.4672	+	4.17372i	−0.705758	+	0.256875i
$265$		0			0
$266$	−8.62266	+	15.3375i	−0.528689	+	0.940402i
$267$		−	32.7229i		−	2.00261i
$268$	−3.76316	−	10.3392i	−0.229872	−	0.631567i
$269$	0.487261	−	2.76340i	0.0297088	−	0.168487i	−0.966343	−	0.257255i	$-0.917182\pi$
$269$	0.487261	−	2.76340i	0.0297088	−	0.168487i	0.996052	+	0.0887681i	$0.0282930\pi$
$270$		0			0
$271$	6.28912	+	5.27720i	0.382037	+	0.320567i	0.813502	−	0.581563i	$-0.197559\pi$
$271$	6.28912	+	5.27720i	0.382037	+	0.320567i	−0.431464	+	0.902130i	$0.642003\pi$
$272$	−1.50865	+	0.266015i	−0.0914752	+	0.0161296i
$273$	−55.8182	+	32.2267i	−3.37827	+	1.95045i
$274$	1.63369	−	2.82963i	0.0986946	−	0.170944i
$275$		0			0
$276$	−16.1987	−	5.89583i	−0.975044	−	0.354887i
$277$	17.4575	+	10.0791i	1.04892	+	0.605595i	0.922347	−	0.386362i	$-0.126268\pi$
$277$	17.4575	+	10.0791i	1.04892	+	0.605595i	0.126574	+	0.991957i	$0.459602\pi$
$278$	1.37053	−	0.791276i	0.0821990	−	0.0474576i
$279$	−2.52596	−	14.3254i	−0.151225	−	0.857641i
$280$		0			0
$281$	3.80083	−	3.18928i	0.226739	−	0.190256i	−0.522340	−	0.852737i	$-0.674941\pi$
$281$	3.80083	−	3.18928i	0.226739	−	0.190256i	0.749079	+	0.662481i	$0.230496\pi$
$282$	−30.0740	−	5.30286i	−1.79088	−	0.315781i
$283$	−5.16552	−	14.1921i	−0.307058	−	0.843635i	−0.993227	−	0.116193i	$-0.962931\pi$
$283$	−5.16552	−	14.1921i	−0.307058	−	0.843635i	0.686168	−	0.727443i	$-0.259291\pi$
$284$	7.48509			0.444159
$285$		0			0
$286$	−23.3369			−1.37994
$287$	4.45275	+	12.2338i	0.262838	+	0.722141i
$288$	5.26818	+	0.928923i	0.310431	+	0.0547373i
$289$	11.2250	−	9.41891i	0.660295	−	0.554053i
$290$		0			0
$291$	6.84828	+	38.8385i	0.401453	+	2.27675i
$292$	−1.70748	+	0.985814i	−0.0999227	+	0.0576904i
$293$	−2.35283	−	1.35841i	−0.137454	−	0.0793589i	0.429696	−	0.902974i	$-0.358621\pi$
$293$	−2.35283	−	1.35841i	−0.137454	−	0.0793589i	−0.567150	+	0.823615i	$0.691954\pi$
$294$	25.2363	+	9.18525i	1.47181	+	0.535695i
$295$		0			0
$296$	−4.35795	+	7.54819i	−0.253301	+	0.438729i
$297$	24.8296	−	14.3354i	1.44076	−	0.831822i
$298$	11.8843	−	2.09553i	0.688441	−	0.121391i
$299$	−25.2533	−	21.1900i	−1.46044	−	1.22545i
$300$		0			0
$301$	−1.59993	+	9.07367i	−0.0922186	+	0.522997i
$302$	1.70482	+	4.68394i	0.0981011	+	0.269531i
$303$		−	41.0865i		−	2.36036i
$304$	4.35861	−	0.0498692i	0.249984	−	0.00286019i
$305$		0			0
$306$	7.70073	−	2.80284i	0.440221	−	0.160227i
$307$	24.9663	+	4.40223i	1.42490	+	0.251248i	0.832335	−	0.554273i	$-0.187004\pi$
$307$	24.9663	+	4.40223i	1.42490	+	0.251248i	0.592566	+	0.805522i	$0.298115\pi$
$308$	10.9579	+	13.0591i	0.624383	+	0.744111i
$309$	−17.7276	−	14.8752i	−1.00849	−	0.846222i
$310$		0			0
$311$	−1.87719	−	3.25139i	−0.106446	−	0.184370i	0.807882	−	0.589344i	$-0.200614\pi$
$311$	−1.87719	−	3.25139i	−0.106446	−	0.184370i	−0.914328	+	0.404974i	$0.867280\pi$
$312$	13.8280	+	7.98361i	0.782857	+	0.451983i
$313$	−7.30618	+	20.0736i	−0.412970	+	1.13463i	0.542634	+	0.839969i	$0.317427\pi$
$313$	−7.30618	+	20.0736i	−0.412970	+	1.13463i	−0.955604	+	0.294656i	$0.904795\pi$
$314$	−14.7258	−	5.35977i	−0.831028	−	0.302469i
$315$		0			0
$316$	−6.21896	−	10.7716i	−0.349844	−	0.605947i
$317$	20.2025	−	3.56224i	1.13468	−	0.200075i	0.425404	−	0.905003i	$-0.360132\pi$
$317$	20.2025	−	3.56224i	1.13468	−	0.200075i	0.709279	+	0.704928i	$0.249021\pi$
$318$	−4.80060	+	5.72114i	−0.269204	+	0.320825i
$319$	−17.1235	+	14.3683i	−0.958733	+	0.804473i
$320$		0			0
$321$	47.6506	−	17.3434i	2.65960	−	0.968014i
$322$			24.0813i			1.34200i
$323$	5.74430	−	3.40469i	0.319621	−	0.189442i
$324$	−3.56828			−0.198238
$325$		0			0
$326$	−1.46084	+	8.28486i	−0.0809087	+	0.458856i
$327$	−14.8303	−	17.6741i	−0.820118	−	0.977378i
$328$	2.07314	−	2.47067i	0.114470	−	0.136420i
$329$	7.40793	+	42.0125i	0.408413	+	2.31622i
$330$		0			0
$331$	−16.3737	+	28.3601i	−0.899982	+	1.55881i	−0.0724661	+	0.997371i	$0.523087\pi$
$331$	−16.3737	+	28.3601i	−0.899982	+	1.55881i	−0.827515	+	0.561443i	$0.810246\pi$
$332$	−1.31257	+	3.60626i	−0.0720367	+	0.197919i
$333$	15.9468	−	43.8134i	0.873878	−	2.40096i
$334$	−1.60132	+	2.77357i	−0.0876203	+	0.151763i
$335$		0			0
$336$	−2.02542	−	11.4867i	−0.110496	−	0.626653i
$337$	−15.3643	+	18.3105i	−0.836948	+	0.997435i	0.162994	+	0.986627i	$0.447885\pi$
$337$	−15.3643	+	18.3105i	−0.836948	+	0.997435i	−0.999942	+	0.0108083i	$0.996560\pi$
$338$	11.2714	+	13.4327i	0.613083	+	0.730644i
$339$	−3.94402	+	22.3677i	−0.214210	+	1.21484i
$340$		0			0
$341$	−11.4839			−0.621889
$342$	−22.9156	+	4.31153i	−1.23914	+	0.233141i
$343$		−	9.26063i		−	0.500027i
$344$	2.14487	−	0.780669i	0.115644	−	0.0420909i
$345$		0			0
$346$	10.8286	−	9.08628i	0.582150	−	0.488482i
$347$	−8.78538	+	10.4700i	−0.471624	+	0.562059i	−0.948445	−	0.316941i	$-0.897344\pi$
$347$	−8.78538	+	10.4700i	−0.471624	+	0.562059i	0.476822	+	0.879000i	$0.341789\pi$
$348$	15.0618	−	2.65580i	0.807397	−	0.142366i
$349$	−12.6829	−	21.9674i	−0.678899	−	1.17589i	−0.975313	−	0.220828i	$-0.929124\pi$
$349$	−12.6829	−	21.9674i	−0.678899	−	1.17589i	0.296414	−	0.955060i	$-0.404209\pi$
$350$		0			0
$351$	−35.2518	−	12.8306i	−1.88160	−	0.684848i
$352$	1.44442	−	3.96852i	0.0769881	−	0.211523i
$353$	−15.6173	−	9.01663i	−0.831223	−	0.479907i	0.0230484	−	0.999734i	$-0.492663\pi$
$353$	−15.6173	−	9.01663i	−0.831223	−	0.479907i	−0.854271	+	0.519828i	$0.825996\pi$
$354$	−15.2283	−	26.3761i	−0.809372	−	1.40187i
$355$		0			0
$356$	8.67515	+	7.27931i	0.459782	+	0.385803i
$357$	−11.4855	−	13.6879i	−0.607876	−	0.724438i
$358$	16.7438	+	2.95239i	0.884939	+	0.156039i
$359$	−15.1395	+	5.51032i	−0.799031	+	0.290824i	−0.709085	−	0.705123i	$-0.750892\pi$
$359$	−15.1395	+	5.51032i	−0.799031	+	0.290824i	−0.0899463	+	0.995947i	$0.528670\pi$
$360$		0			0
$361$	−17.7008	+	6.90519i	−0.931621	+	0.363431i
$362$		−	19.9527i		−	1.04869i
$363$	−6.75544	−	18.5604i	−0.354569	−	0.974169i
$364$	3.87335	−	21.9669i	0.203019	−	1.15138i
$365$		0			0
$366$	−9.97264	−	8.36804i	−0.521278	−	0.437404i
$367$	9.75596	−	1.72024i	0.509257	−	0.0897957i	0.0868849	−	0.996218i	$-0.472309\pi$
$367$	9.75596	−	1.72024i	0.509257	−	0.0897957i	0.422372	+	0.906423i	$0.361198\pi$
$368$	5.16648	−	2.98287i	0.269321	−	0.155493i
$369$	−8.62661	+	14.9417i	−0.449084	+	0.777835i
$370$		0			0
$371$	9.80395	+	3.56835i	0.508996	+	0.185259i
$372$	6.80466	+	3.92867i	0.352805	+	0.203692i
$373$	7.58731	−	4.38054i	0.392856	−	0.226816i	−0.290541	−	0.956863i	$-0.593835\pi$
$373$	7.58731	−	4.38054i	0.392856	−	0.226816i	0.683397	+	0.730047i	$0.260502\pi$
$374$	−1.12344	−	6.37135i	−0.0580917	−	0.329454i
$375$		0			0
$376$	8.09589	−	6.79326i	0.417514	−	0.350336i
$377$	28.8037	+	5.07886i	1.48346	+	0.261575i
$378$	9.37267	+	25.7512i	0.482078	+	1.32450i
$379$	−9.49485			−0.487718			−0.243859	−	0.969811i	$-0.578413\pi$
$379$	−9.49485			−0.487718			−0.243859	+	0.969811i	$0.578413\pi$
$380$		0			0
$381$	53.6064			2.74634
$382$	3.44536	+	9.46604i	0.176280	+	0.484325i
$383$	−28.8836	−	5.09296i	−1.47588	−	0.260238i	−0.622952	−	0.782260i	$-0.714067\pi$
$383$	−28.8836	−	5.09296i	−1.47588	−	0.260238i	−0.852932	+	0.522022i	$0.825178\pi$
$384$	−2.21352	+	1.85736i	−0.112958	+	0.0947831i
$385$		0			0
$386$	0.799380	+	4.53351i	0.0406874	+	0.230750i
$387$	−10.5744	+	6.10513i	−0.537526	+	0.310341i
$388$	−11.8199	−	6.82421i	−0.600063	−	0.346447i
$389$	11.3431	+	4.12854i	0.575117	+	0.209325i	0.613171	−	0.789950i	$-0.289894\pi$
$389$	11.3431	+	4.12854i	0.575117	+	0.209325i	−0.0380542	+	0.999276i	$0.512116\pi$
$390$		0			0
$391$	4.56952	−	7.91464i	0.231091	−	0.400261i
$392$	−8.04898	+	4.64708i	−0.406535	+	0.234713i
$393$	27.9284	−	4.92452i	1.40880	−	0.248409i
$394$	0.832311	+	0.698392i	0.0419312	+	0.0351845i
$395$		0			0
$396$	−3.92304	+	22.2487i	−0.197140	+	1.11804i
$397$	−3.91763	−	10.7636i	−0.196620	−	0.540210i	0.801726	−	0.597691i	$-0.203915\pi$
$397$	−3.91763	−	10.7636i	−0.196620	−	0.540210i	−0.998347	+	0.0574815i	$0.981693\pi$
$398$		−	1.29976i		−	0.0651509i
$399$	25.9230	+	43.7367i	1.29777	+	2.18957i
$400$		0			0
$401$	4.66865	−	1.69925i	0.233141	−	0.0848564i	−0.222808	−	0.974862i	$-0.571522\pi$
$401$	4.66865	−	1.69925i	0.233141	−	0.0848564i	0.455949	+	0.890006i	$0.349300\pi$
$402$	−31.3099	−	5.52078i	−1.56159	−	0.275351i
$403$	9.65861	+	11.5107i	0.481130	+	0.573388i
$404$	10.8924	+	9.13983i	0.541918	+	0.454723i
$405$		0			0
$406$	−10.6827	−	18.5030i	−0.530175	−	0.918290i
$407$	−31.8776	−	18.4045i	−1.58011	−	0.912280i
$408$	−1.51397	+	4.15960i	−0.0749527	+	0.205931i
$409$	1.22014	+	0.444093i	0.0603318	+	0.0219590i	0.372010	−	0.928229i	$-0.378669\pi$
$409$	1.22014	+	0.444093i	0.0603318	+	0.0219590i	−0.311678	+	0.950188i	$0.600891\pi$
$410$		0			0
$411$	−4.72061	−	8.17633i	−0.232850	−	0.403309i
$412$	7.88712	−	1.39071i	0.388571	−	0.0685155i
$413$	−27.3486	+	32.5928i	−1.34573	+	1.60378i
$414$	−24.4471	+	20.5136i	−1.20151	+	1.00819i
$415$		0			0
$416$	−5.19261	+	1.88996i	−0.254589	+	0.0926628i
$417$		−	4.57285i		−	0.223934i
$418$	0.210608	+	18.4074i	0.0103012	+	0.900333i
$419$	36.1438			1.76574			0.882870	−	0.469617i	$-0.155608\pi$
$419$	36.1438			1.76574			0.882870	+	0.469617i	$0.155608\pi$
$420$		0			0
$421$	−5.28902	+	29.9955i	−0.257771	+	1.46189i	0.531088	+	0.847317i	$0.321783\pi$
$421$	−5.28902	+	29.9955i	−0.257771	+	1.46189i	−0.788859	+	0.614574i	$0.789328\pi$
$422$	−3.32975	−	3.96824i	−0.162089	−	0.193171i
$423$	−36.3402	+	43.3086i	−1.76692	+	2.10574i
$424$	−0.448817	−	2.54537i	−0.0217965	−	0.123614i
$425$		0			0
$426$	10.8142	−	18.7308i	0.523952	−	0.907511i
$427$	−6.22007	+	17.0895i	−0.301010	+	0.827018i
$428$	−6.00213	+	16.4907i	−0.290124	+	0.797108i
$429$	−33.7165	+	58.3987i	−1.62785	+	2.81952i
$430$		0			0
$431$	−6.25630	−	35.4813i	−0.301355	−	1.70907i	−0.640182	−	0.768223i	$-0.721141\pi$
$431$	−6.25630	−	35.4813i	−0.301355	−	1.70907i	0.338827	−	0.940849i	$-0.389970\pi$
$432$	4.36378	−	5.20055i	0.209953	−	0.250212i
$433$	18.7188	+	22.3082i	0.899568	+	1.07206i	0.997045	+	0.0768258i	$0.0244785\pi$
$433$	18.7188	+	22.3082i	0.899568	+	1.07206i	−0.0974763	+	0.995238i	$0.531077\pi$
$434$	1.90605	−	10.8097i	0.0914931	−	0.518883i
$435$		0			0
$436$	7.98461			0.382393
$437$	−16.4861	+	20.1102i	−0.788636	+	0.962001i
$438$			5.69710i			0.272218i
$439$	3.06643	−	1.11609i	0.146353	−	0.0532681i	−0.267805	−	0.963473i	$-0.586298\pi$
$439$	3.06643	−	1.11609i	0.146353	−	0.0532681i	0.414158	+	0.910205i	$0.364076\pi$
$440$		0			0
$441$	38.0867	−	31.9586i	1.81365	−	1.52184i
$442$	−5.44132	+	6.48471i	−0.258817	+	0.308446i
$443$	33.5612	−	5.91774i	1.59454	−	0.281160i	0.695334	−	0.718687i	$-0.255256\pi$
$443$	33.5612	−	5.91774i	1.59454	−	0.281160i	0.899206	+	0.437526i	$0.144145\pi$
$444$	12.5925	+	21.8108i	0.597612	+	1.03509i
$445$		0			0
$446$	−7.60083	−	2.76648i	−0.359910	−	0.130996i
$447$	11.9263	−	32.7671i	0.564093	−	1.54983i
$448$	3.49580	+	2.01830i	0.165161	+	0.0953558i
$449$	16.0584	+	27.8139i	0.757841	+	1.31262i	0.943950	+	0.330089i	$0.107079\pi$
$449$	16.0584	+	27.8139i	0.757841	+	1.31262i	−0.186109	+	0.982529i	$0.559588\pi$
$450$		0			0
$451$	10.4342	+	8.75531i	0.491326	+	0.412272i
$452$	−5.05251	−	6.02135i	−0.237650	−	0.283221i
$453$	14.1842	+	2.50106i	0.666434	+	0.117510i
$454$	6.14020	−	2.23485i	0.288174	−	0.104887i
$455$		0			0
$456$	6.17240	−	10.9791i	0.289049	−	0.514144i
$457$		−	8.66519i		−	0.405341i	−0.979247	−	0.202670i	$-0.935038\pi$
$457$		−	8.66519i		−	0.405341i	0.979247	−	0.202670i	$-0.0649620\pi$
$458$	−8.85478	−	24.3283i	−0.413756	−	1.13679i
$459$	1.80594	−	10.2420i	0.0842939	−	0.478054i
$460$		0			0
$461$	−13.5892	−	11.4027i	−0.632911	−	0.531076i	0.268921	−	0.963162i	$-0.413333\pi$
$461$	−13.5892	−	11.4027i	−0.632911	−	0.531076i	−0.901832	+	0.432087i	$0.857777\pi$
$462$	48.5109	−	8.55379i	2.25693	−	0.397958i
$463$	−22.9510	+	13.2507i	−1.06662	+	0.615814i	−0.927257	−	0.374427i	$-0.877840\pi$
$463$	−22.9510	+	13.2507i	−1.06662	+	0.615814i	−0.139365	+	0.990241i	$0.544506\pi$
$464$	−2.64646	+	4.58381i	−0.122859	+	0.212798i
$465$		0			0
$466$	21.3317	+	7.76411i	0.988173	+	0.359665i
$467$	13.6094	+	7.85739i	0.629768	+	0.363597i	0.780662	−	0.624953i	$-0.214882\pi$
$467$	13.6094	+	7.85739i	0.629768	+	0.363597i	−0.150894	+	0.988550i	$0.548215\pi$
$468$	25.6000	−	14.7802i	1.18336	−	0.683214i
$469$	7.71236	+	43.7390i	0.356124	+	2.01968i
$470$		0			0
$471$	−34.6879	+	29.1066i	−1.59833	+	1.34116i
$472$	10.3801	+	1.83030i	0.477784	+	0.0842462i
$473$	3.29693	+	9.05825i	0.151593	+	0.416499i
$474$	−35.9399			−1.65077
$475$		0			0
$476$	6.18376			0.283432
$477$	4.72890	+	12.9926i	0.216522	+	0.594888i
$478$	−8.82152	−	1.55547i	−0.403487	−	0.0711456i
$479$	7.03049	−	5.89928i	0.321231	−	0.269545i	−0.467884	−	0.883790i	$-0.654984\pi$
$479$	7.03049	−	5.89928i	0.321231	−	0.269545i	0.789116	+	0.614245i	$0.210539\pi$
$480$		0			0
$481$	8.36339	+	47.4312i	0.381338	+	2.16267i
$482$	−2.90508	+	1.67725i	−0.132323	+	0.0763965i
$483$	60.2615	+	34.7920i	2.74199	+	1.58309i
$484$	6.42331	+	2.33789i	0.291968	+	0.106268i
$485$		0			0
$486$	5.02791	−	8.70859i	0.228071	−	0.395030i
$487$	23.0303	−	13.2965i	1.04360	−	0.602524i	0.122751	−	0.992438i	$-0.460828\pi$
$487$	23.0303	−	13.2965i	1.04360	−	0.602524i	0.920852	+	0.389913i	$0.127495\pi$
$488$	4.43689	−	0.782343i	0.200849	−	0.0354150i
$489$	18.6216	+	15.6254i	0.842097	+	0.706603i
$490$		0			0
$491$	−5.89000	+	33.4038i	−0.265812	+	1.50749i	0.500901	+	0.865504i	$0.333002\pi$
$491$	−5.89000	+	33.4038i	−0.265812	+	1.50749i	−0.766713	+	0.641990i	$0.778109\pi$
$492$	−3.18744	−	8.75741i	−0.143701	−	0.394815i
$493$			8.10835i			0.365182i
$494$	18.2731	−	15.6927i	0.822147	−	0.706048i
$495$		0			0
$496$	−2.55525	+	0.930034i	−0.114734	+	0.0417597i
$497$	−29.7553	−	5.24667i	−1.33471	−	0.235345i
$498$	7.12800	+	8.49482i	0.319413	+	0.380662i
$499$	21.1761	+	17.7689i	0.947973	+	0.795444i	0.978955	−	0.204076i	$-0.0654190\pi$
$499$	21.1761	+	17.7689i	0.947973	+	0.795444i	−0.0309820	+	0.999520i	$0.509863\pi$
$500$		0			0
$501$	4.62708	+	8.01433i	0.206723	+	0.358054i
$502$	19.3272	+	11.1586i	0.862616	+	0.498032i
$503$	−7.38317	+	20.2851i	−0.329199	+	0.904468i	0.659116	+	0.752042i	$0.270931\pi$
$503$	−7.38317	+	20.2851i	−0.329199	+	0.904468i	−0.988315	+	0.152426i	$0.951291\pi$
$504$	−20.2914	−	7.38545i	−0.903849	−	0.328974i
$505$		0			0
$506$	12.5973	+	21.8192i	0.560018	+	0.969980i
$507$	49.8989	−	8.79852i	2.21609	−	0.390756i
$508$	−11.9249	+	14.2116i	−0.529083	+	0.630536i
$509$	1.78133	−	1.49471i	0.0789560	−	0.0662520i	−0.602455	−	0.798152i	$-0.705811\pi$
$509$	1.78133	−	1.49471i	0.0789560	−	0.0662520i	0.681411	+	0.731901i	$0.261366\pi$
$510$		0			0
$511$	7.47871	−	2.72203i	0.330839	−	0.120415i
$512$		−	1.00000i		−	0.0441942i
$513$	−9.80222	+	27.9212i	−0.432778	+	1.23275i
$514$	0.933658			0.0411819
$515$		0			0
$516$	1.14529	−	6.49525i	0.0504185	−	0.285937i
$517$	28.6894	+	34.1907i	1.26176	+	1.50371i
$518$	22.6149	−	26.9514i	0.993644	−	1.18418i
$519$	−7.09280	−	40.2253i	−0.311340	−	1.76569i
$520$		0			0
$521$	2.81228	−	4.87102i	0.123208	−	0.213403i	−0.797823	−	0.602892i	$-0.794015\pi$
$521$	2.81228	−	4.87102i	0.123208	−	0.213403i	0.921031	+	0.389489i	$0.127348\pi$
$522$	9.68405	−	26.6067i	0.423859	−	1.16454i
$523$	14.2976	−	39.2824i	0.625192	−	1.71770i	−0.0687164	−	0.997636i	$-0.521890\pi$
$523$	14.2976	−	39.2824i	0.625192	−	1.71770i	0.693908	−	0.720064i	$-0.255887\pi$
$524$	−4.90721	+	8.49954i	−0.214373	+	0.371304i
$525$		0			0
$526$	2.57491	+	14.6030i	0.112271	+	0.636723i
$527$	−2.67763	+	3.19108i	−0.116640	+	0.139006i
$528$	−7.84404	−	9.34816i	−0.341368	−	0.406826i
$529$	−2.18623	+	12.3987i	−0.0950536	+	0.539076i
$530$		0			0
$531$	−56.3846			−2.44688
$532$	−17.3617	−	2.85692i	−0.752723	−	0.123863i
$533$		−	17.8222i		−	0.771965i
$534$	30.7495	−	11.1919i	1.33066	−	0.484321i
$535$		0			0
$536$	8.42859	−	7.07243i	0.364060	−	0.305482i
$537$	31.5791	−	37.6345i	1.36274	−	1.62405i
$538$	2.76340	−	0.487261i	0.119138	−	0.0210073i
$539$	−19.6256	−	33.9926i	−0.845335	−	1.46416i
$540$		0			0
$541$	19.0797	+	6.94444i	0.820300	+	0.298565i	0.717871	−	0.696176i	$-0.245117\pi$
$541$	19.0797	+	6.94444i	0.820300	+	0.298565i	0.102428	+	0.994740i	$0.467339\pi$
$542$	−2.80794	+	7.71475i	−0.120611	+	0.331377i
$543$	−49.9300	−	28.8271i	−2.14270	−	1.23709i
$544$	−0.765961	−	1.32668i	−0.0328403	−	0.0568811i
$545$		0			0
$546$	−49.3741	−	41.4298i	−2.11302	−	1.77303i
$547$	−23.7651	−	28.3221i	−1.01612	−	1.21097i	−0.977330	−	0.211720i	$-0.932093\pi$
$547$	−23.7651	−	28.3221i	−1.01612	−	1.21097i	−0.0387920	−	0.999247i	$-0.512351\pi$
$548$	3.21773	+	0.567373i	0.137455	+	0.0242370i
$549$	−22.6476	+	8.24306i	−0.966576	+	0.351805i
$550$		0			0
$551$	3.74609	−	22.7652i	0.159589	−	0.969829i
$552$		−	17.2382i		−	0.733708i
$553$	17.1718	+	47.1791i	0.730219	+	2.00626i
$554$	−3.50044	+	19.8520i	−0.148719	+	0.843430i
$555$		0			0
$556$	1.21231	+	1.01725i	0.0514132	+	0.0431408i
$557$	12.2041	−	2.15190i	0.517102	−	0.0911791i	0.0909943	−	0.995851i	$-0.470995\pi$
$557$	12.2041	−	2.15190i	0.517102	−	0.0911791i	0.426108	+	0.904672i	$0.359884\pi$
$558$	12.5976	−	7.27321i	0.533298	−	0.307900i
$559$	6.30646	−	10.9231i	0.266735	−	0.461998i
$560$		0			0
$561$	−17.5669	−	6.39382i	−0.741674	−	0.269947i
$562$	4.29690	+	2.48082i	0.181254	+	0.104647i
$563$	8.54424	−	4.93302i	0.360097	−	0.207902i	−0.309027	−	0.951053i	$-0.600003\pi$
$563$	8.54424	−	4.93302i	0.360097	−	0.207902i	0.669123	+	0.743152i	$0.266670\pi$
$564$	−5.30286	−	30.0740i	−0.223291	−	1.26634i
$565$		0			0
$566$	11.5695	−	9.70800i	0.486304	−	0.408058i
$567$	14.1849	+	2.50118i	0.595711	+	0.105040i
$568$	2.56005	+	7.03369i	0.107417	+	0.295127i
$569$	−15.2083			−0.637565			−0.318782	−	0.947828i	$-0.603274\pi$
$569$	−15.2083			−0.637565			−0.318782	+	0.947828i	$0.603274\pi$
$570$		0			0
$571$	−26.6461			−1.11511			−0.557553	−	0.830141i	$-0.688260\pi$
$571$	−26.6461			−1.11511			−0.557553	+	0.830141i	$0.688260\pi$
$572$	−7.98169	−	21.9295i	−0.333731	−	0.916920i
$573$	28.6657	+	5.05454i	1.19753	+	0.211156i
$574$	−9.97312	+	8.36844i	−0.416270	+	0.349292i
$575$		0			0
$576$	0.928923	+	5.26818i	0.0387051	+	0.219508i
$577$	−29.6874	+	17.1401i	−1.23590	+	0.713550i	−0.968254	−	0.249967i	$-0.919580\pi$
$577$	−29.6874	+	17.1401i	−1.23590	+	0.713550i	−0.267650	+	0.963516i	$0.586247\pi$
$578$	12.6901	+	7.32661i	0.527837	+	0.304747i
$579$	12.4997	+	4.54950i	0.519468	+	0.189071i
$580$		0			0
$581$	7.74564	−	13.4158i	0.321343	−	0.556583i
$582$	−34.1540	+	19.7188i	−1.41573	+	0.817372i
$583$	10.7496	−	1.89545i	0.445205	−	0.0785016i
$584$	−1.51035	−	1.26734i	−0.0624989	−	0.0524428i
$585$		0			0
$586$	0.471769	−	2.67554i	0.0194886	−	0.110525i
$587$	10.9423	+	30.0636i	0.451636	+	1.24086i	0.931572	+	0.363556i	$0.118437\pi$
$587$	10.9423	+	30.0636i	0.451636	+	1.24086i	−0.479937	+	0.877303i	$0.659340\pi$
$588$			26.8559i			1.10752i
$589$	8.99207	−	7.72226i	0.370512	−	0.318190i
$590$		0			0
$591$	2.95016	−	1.07377i	0.121354	−	0.0441691i
$592$	−8.58348	−	1.51350i	−0.352779	−	0.0622044i
$593$	−10.8774	−	12.9632i	−0.446683	−	0.532336i	0.494975	−	0.868907i	$-0.335177\pi$
$593$	−10.8774	−	12.9632i	−0.446683	−	0.532336i	−0.941658	+	0.336571i	$0.890733\pi$
$594$	21.9631	+	18.4292i	0.901155	+	0.756159i
$595$		0			0
$596$	6.03384	+	10.4509i	0.247156	+	0.428086i
$597$	−3.25253	−	1.87785i	−0.133117	−	0.0768554i
$598$	11.2750	−	30.9778i	0.461069	−	1.26678i
$599$	−16.3401	−	5.94730i	−0.667637	−	0.243000i	−0.0141069	−	0.999900i	$-0.504491\pi$
$599$	−16.3401	−	5.94730i	−0.667637	−	0.243000i	−0.653530	+	0.756901i	$0.726713\pi$
$600$		0			0
$601$	2.18870	+	3.79093i	0.0892787	+	0.154635i	0.907206	−	0.420686i	$-0.138210\pi$
$601$	2.18870	+	3.79093i	0.0892787	+	0.154635i	−0.817928	+	0.575321i	$0.804877\pi$
$602$	−9.07367	+	1.59993i	−0.369815	+	0.0652084i
$603$	−37.8336	+	45.0883i	−1.54070	+	1.83614i
$604$	−3.81838	+	3.20400i	−0.155368	+	0.130369i
$605$		0			0
$606$	38.6087	−	14.0524i	1.56837	−	0.570841i
$607$			36.1181i			1.46599i	0.680234	+	0.732995i	$0.261878\pi$
$607$			36.1181i			1.46599i	−0.680234	+	0.732995i	$0.738122\pi$
$608$	1.53760	+	4.07870i	0.0623577	+	0.165413i
$609$	−61.7364			−2.50168
$610$		0			0
$611$	10.1410	−	57.5126i	0.410262	−	2.32671i
$612$	5.26761	+	6.27769i	0.212930	+	0.253761i
$613$	−8.07763	+	9.62654i	−0.326252	+	0.388812i	−0.904092	−	0.427338i	$-0.859451\pi$
$613$	−8.07763	+	9.62654i	−0.326252	+	0.388812i	0.577840	+	0.816150i	$0.303896\pi$
$614$	4.40223	+	24.9663i	0.177660	+	1.00756i
$615$		0			0
$616$	−8.52372	+	14.7635i	−0.343430	+	0.594839i
$617$	−8.14855	+	22.3880i	−0.328048	+	0.901305i	0.660557	+	0.750776i	$0.270320\pi$
$617$	−8.14855	+	22.3880i	−0.328048	+	0.901305i	−0.988605	+	0.150530i	$0.951902\pi$
$618$	7.91494	−	21.7461i	0.318386	−	0.874757i
$619$	−0.743546	+	1.28786i	−0.0298856	+	0.0517635i	−0.880581	−	0.473895i	$-0.842848\pi$
$619$	−0.743546	+	1.28786i	−0.0298856	+	0.0517635i	0.850696	+	0.525658i	$0.176181\pi$
$620$		0			0
$621$	7.03283	+	39.8851i	0.282218	+	1.60054i
$622$	2.41327	−	2.87603i	0.0967634	−	0.115318i
$623$	−29.3837	−	35.0181i	−1.17723	−	1.40297i
$624$	−2.77268	+	15.7246i	−0.110996	+	0.629489i
$625$		0			0
$626$	−21.3618			−0.853791
$627$	46.3672	+	26.0674i	1.85173	+	1.04103i
$628$		−	15.6709i		−	0.625338i
$629$	−12.5468	+	4.56668i	−0.500275	+	0.182085i
$630$		0			0
$631$	20.1333	−	16.8939i	0.801495	−	0.672534i	−0.147067	−	0.989127i	$-0.546983\pi$
$631$	20.1333	−	16.8939i	0.801495	−	0.672534i	0.948562	+	0.316592i	$0.102539\pi$
$632$	7.99494	−	9.52800i	0.318022	−	0.379003i
$633$	−14.7409	+	2.59922i	−0.585898	+	0.103310i
$634$	10.2571	+	17.7657i	0.407360	+	0.705568i
$635$		0			0
$636$	−7.01801	−	2.55435i	−0.278282	−	0.101286i
$637$	−17.5656	+	48.2610i	−0.695973	+	1.91217i
$638$	−19.3584	−	11.1766i	−0.766407	−	0.442485i
$639$	−20.0206	−	34.6767i	−0.792002	−	1.37179i
$640$		0			0
$641$	−3.77655	−	3.16890i	−0.149165	−	0.125164i	0.565151	−	0.824987i	$-0.308818\pi$
$641$	−3.77655	−	3.16890i	−0.149165	−	0.125164i	−0.714316	+	0.699823i	$0.753262\pi$
$642$	32.5949	+	38.8451i	1.28642	+	1.53309i
$643$	−7.58704	−	1.33780i	−0.299204	−	0.0527577i	0.0220310	−	0.999757i	$-0.492987\pi$
$643$	−7.58704	−	1.33780i	−0.299204	−	0.0527577i	−0.321235	+	0.947000i	$0.604098\pi$
$644$	−22.6290	+	8.23629i	−0.891709	+	0.324555i
$645$		0			0
$646$	5.16403	+	4.23341i	0.203176	+	0.166561i
$647$			33.7875i			1.32832i	0.747590	+	0.664161i	$0.231211\pi$
$647$			33.7875i			1.32832i	−0.747590	+	0.664161i	$0.768789\pi$
$648$	−1.22042	−	3.35309i	−0.0479428	−	0.131722i
$649$	−7.72973	+	43.8375i	−0.303418	+	1.72077i
$650$		0			0
$651$	−24.2966	−	20.3873i	−0.952260	−	0.799041i
$652$	−8.28486	+	1.46084i	−0.324460	+	0.0572111i
$653$	10.7184	−	6.18826i	0.419442	−	0.242165i	−0.275396	−	0.961331i	$-0.588809\pi$
$653$	10.7184	−	6.18826i	0.419442	−	0.242165i	0.694839	+	0.719166i	$0.255476\pi$
$654$	11.5359	−	19.9808i	0.451091	−	0.781312i
$655$		0			0
$656$	3.03073	+	1.10309i	0.118330	+	0.0430686i
$657$	9.13408	+	5.27357i	0.356355	+	0.205741i
$658$	−36.9452	+	21.3303i	−1.44027	+	0.831542i
$659$	−1.69829	−	9.63145i	−0.0661558	−	0.375188i	−0.999853	−	0.0171255i	$-0.994549\pi$
$659$	−1.69829	−	9.63145i	−0.0661558	−	0.375188i	0.933698	−	0.358063i	$-0.116563\pi$
$660$		0			0
$661$	13.0726	−	10.9692i	0.508466	−	0.426654i	−0.352123	−	0.935954i	$-0.614540\pi$
$661$	13.0726	−	10.9692i	0.508466	−	0.426654i	0.860589	+	0.509300i	$0.170096\pi$
$662$	−32.2500	−	5.68654i	−1.25343	−	0.221014i
$663$	8.36599	+	22.9854i	0.324908	+	0.892678i
$664$	−3.83770			−0.148932
$665$		0			0
$666$	46.6253			1.80669
$667$	−10.7997	−	29.6719i	−0.418166	−	1.14890i
$668$	−3.15398	−	0.556132i	−0.122031	−	0.0215174i
$669$	−17.9043	+	15.0235i	−0.692221	+	0.580843i
$670$		0			0
$671$	3.30400	+	18.7379i	0.127550	+	0.723370i
$672$	10.1013	−	5.83197i	0.389665	−	0.224973i
$673$	−21.1903	−	12.2342i	−0.816826	−	0.471595i	0.0324944	−	0.999472i	$-0.489655\pi$
$673$	−21.1903	−	12.2342i	−0.816826	−	0.471595i	−0.849321	+	0.527877i	$0.822988\pi$
$674$	−22.4611	−	8.17518i	−0.865170	−	0.314896i
$675$		0			0
$676$	−8.76759	+	15.1859i	−0.337215	+	0.584074i
$677$	2.20353	−	1.27221i	0.0846884	−	0.0488949i	−0.457058	−	0.889437i	$-0.651097\pi$
$677$	2.20353	−	1.27221i	0.0846884	−	0.0488949i	0.541746	+	0.840542i	$0.317763\pi$
$678$	−22.3677	+	3.94402i	−0.859025	+	0.151469i
$679$	42.2039	+	35.4132i	1.61964	+	1.35904i
$680$		0			0
$681$	3.27866	−	18.5942i	0.125638	−	0.712531i
$682$	−3.92773	−	10.7914i	−0.150401	−	0.413222i
$683$		−	13.2825i		−	0.508240i	−0.967173	−	0.254120i	$-0.918214\pi$
$683$		−	13.2825i		−	0.508240i	0.967173	−	0.254120i	$-0.0817857\pi$
$684$	−11.8891	−	20.0590i	−0.454592	−	0.766976i
$685$		0			0
$686$	8.70214	−	3.16732i	0.332249	−	0.120929i
$687$	−73.6727	−	12.9905i	−2.81079	−	0.495618i
$688$	1.46718	+	1.74851i	0.0559356	+	0.0666615i
$689$	−10.9409	−	9.18052i	−0.416816	−	0.349750i
$690$		0			0
$691$	3.25288	+	5.63415i	0.123745	+	0.214333i	0.921242	−	0.388990i	$-0.127176\pi$
$691$	3.25288	+	5.63415i	0.123745	+	0.214333i	−0.797497	+	0.603324i	$0.793843\pi$
$692$	12.2419	+	7.06787i	0.465368	+	0.268680i
$693$	31.1903	−	85.6948i	1.18482	−	3.25528i
$694$	−12.8434	−	4.67460i	−0.487527	−	0.177445i
$695$		0			0
$696$	7.64707	+	13.2451i	0.289861	+	0.502055i
$697$	4.86574	−	0.857961i	0.184303	−	0.0324976i
$698$	16.3048	−	19.4313i	0.617145	−	0.735485i
$699$	50.2485	−	42.1635i	1.90057	−	1.59477i
$700$		0			0
$701$	−5.89524	+	2.14569i	−0.222660	+	0.0810417i	−0.450941	−	0.892554i	$-0.648912\pi$
$701$	−5.89524	+	2.14569i	−0.222660	+	0.0810417i	0.228281	+	0.973595i	$0.426689\pi$
$702$		−	37.5142i		−	1.41588i
$703$	37.3366	−	7.02481i	1.40818	−	0.264946i
$704$	4.22321			0.159168
$705$		0			0
$706$	3.13144	−	17.7593i	0.117853	−	0.668380i
$707$	−36.8939	−	43.9684i	−1.38754	−	1.65360i
$708$	19.5771	−	23.3310i	0.735751	−	0.876834i
$709$	−1.34174	−	7.60941i	−0.0503903	−	0.285777i	0.949191	−	0.314699i	$-0.101904\pi$
$709$	−1.34174	−	7.60941i	−0.0503903	−	0.285777i	−0.999582	+	0.0289219i	$0.990793\pi$
$710$		0			0
$711$	−33.2680	+	57.6219i	−1.24765	+	2.16099i
$712$	−3.87324	+	10.6416i	−0.145156	+	0.398812i
$713$	5.54834	−	15.2439i	0.207787	−	0.570890i
$714$	8.93412	−	15.4743i	0.334351	−	0.579113i
$715$		0			0
$716$	2.95239	+	16.7438i	0.110336	+	0.625746i
$717$	−16.6375	+	19.8278i	−0.621339	+	0.740483i
$718$	−10.3560	−	12.3418i	−0.386483	−	0.460593i
$719$	1.92572	−	10.9213i	0.0718173	−	0.407296i	−0.927613	−	0.373543i	$-0.878143\pi$
$719$	1.92572	−	10.9213i	0.0718173	−	0.407296i	0.999430	−	0.0337534i	$-0.0107461\pi$
$720$		0			0
$721$	−32.3283			−1.20397
$722$	−12.5428	−	14.2716i	−0.466794	−	0.531134i
$723$			9.69296i			0.360485i
$724$	18.7494	−	6.82423i	0.696817	−	0.253621i
$725$		0			0
$726$	15.1306	−	12.6961i	0.561549	−	0.471195i
$727$	−19.0466	+	22.6989i	−0.706401	+	0.841855i	−0.993235	−	0.116125i	$-0.962953\pi$
$727$	−19.0466	+	22.6989i	−0.706401	+	0.841855i	0.286834	+	0.957980i	$0.407397\pi$
$728$	21.9669	−	3.87335i	0.814146	−	0.143556i
$729$	−19.8808	−	34.4345i	−0.736325	−	1.27535i
$730$		0			0
$731$	3.28577	+	1.19592i	0.121529	+	0.0442328i
$732$	4.45254	−	12.2333i	0.164571	−	0.452154i
$733$	22.9943	+	13.2758i	0.849314	+	0.490352i	0.860419	−	0.509587i	$-0.170202\pi$
$733$	22.9943	+	13.2758i	0.849314	+	0.490352i	−0.0111055	+	0.999938i	$0.503535\pi$
$734$	4.95323	+	8.57924i	0.182827	+	0.316666i
$735$		0			0
$736$	4.57002	+	3.83470i	0.168453	+	0.141349i
$737$	29.8684	+	35.5957i	1.10022	+	1.31119i
$738$	−16.9911	−	2.99599i	−0.625451	−	0.110284i
$739$	16.6006	−	6.04212i	0.610663	−	0.222263i	−0.0181306	−	0.999836i	$-0.505771\pi$
$739$	16.6006	−	6.04212i	0.610663	−	0.222263i	0.628793	+	0.777573i	$0.283549\pi$
$740$		0			0
$741$	−12.8692	−	68.3994i	−0.472762	−	2.51271i
$742$			10.4331i			0.383013i
$743$	−2.83848	−	7.79867i	−0.104134	−	0.286105i	0.876673	−	0.481086i	$-0.159758\pi$
$743$	−2.83848	−	7.79867i	−0.104134	−	0.286105i	−0.980807	+	0.194981i	$0.937535\pi$
$744$	−1.36441	+	7.73798i	−0.0500219	+	0.283688i
$745$		0			0
$746$	6.71137	+	5.63151i	0.245721	+	0.206184i
$747$	20.2177	−	3.56493i	0.739727	−	0.130434i
$748$	5.60287	−	3.23482i	0.204861	−	0.118277i
$749$	35.4193	−	61.3480i	1.29419	−	2.24161i
$750$		0			0
$751$	−3.43969	−	1.25195i	−0.125516	−	0.0456841i	0.278498	−	0.960437i	$-0.410163\pi$
$751$	−3.43969	−	1.25195i	−0.125516	−	0.0456841i	−0.404015	+	0.914753i	$0.632386\pi$
$752$	9.15254	+	5.28422i	0.333759	+	0.192696i
$753$	55.8468	−	32.2432i	2.03517	−	1.17501i
$754$	5.07886	+	28.8037i	0.184961	+	1.04897i
$755$		0			0
$756$	−20.9926	+	17.6149i	−0.763492	+	0.640646i
$757$	39.8461	+	7.02594i	1.44823	+	0.255362i	0.841807	−	0.539779i	$-0.181492\pi$
$757$	39.8461	+	7.02594i	1.44823	+	0.255362i	0.606424	+	0.795141i	$0.292603\pi$
$758$	−3.24743	−	8.92224i	−0.117952	−	0.324070i
$759$	72.8008			2.64250
$760$		0			0
$761$	−16.2575			−0.589335			−0.294667	−	0.955600i	$-0.595209\pi$
$761$	−16.2575			−0.589335			−0.294667	+	0.955600i	$0.595209\pi$
$762$	18.3345	+	50.3736i	0.664188	+	1.82484i
$763$	−31.7410	−	5.59680i	−1.14910	−	0.202618i
$764$	−7.71678	+	6.47515i	−0.279183	+	0.234263i
$765$		0			0
$766$	−5.09296	−	28.8836i	−0.184016	−	1.04361i
$767$	50.4408	−	29.1220i	1.82131	−	1.05153i
$768$	−2.50242	−	1.44477i	−0.0902982	−	0.0521337i
$769$	−4.84451	−	1.76326i	−0.174697	−	0.0635846i	0.253191	−	0.967416i	$-0.418520\pi$
$769$	−4.84451	−	1.76326i	−0.174697	−	0.0635846i	−0.427888	+	0.903832i	$0.640742\pi$
$770$		0			0
$771$	1.34892	−	2.33640i	0.0485802	−	0.0841434i
$772$	−3.98670	+	2.30172i	−0.143485	+	0.0828409i
$773$	−34.6179	+	6.10407i	−1.24512	+	0.219548i	−0.757109	−	0.653289i	$-0.773389\pi$
$773$	−34.6179	+	6.10407i	−1.24512	+	0.219548i	−0.488012	+	0.872837i	$0.662278\pi$
$774$	−9.35359	−	7.84860i	−0.336208	−	0.282112i
$775$		0			0
$776$	2.37002	−	13.4411i	0.0850788	−	0.482506i
$777$	−34.7703	−	95.5307i	−1.24738	−	3.42714i
$778$			12.0710i			0.432768i
$779$	−14.0575	+	0.160840i	−0.503664	+	0.00576268i
$780$		0			0
$781$	−29.7048	+	10.8117i	−1.06292	+	0.386871i
$782$	9.00020	+	1.58698i	0.321846	+	0.0567502i
$783$	−23.0972	−	27.5262i	−0.825426	−	0.983705i
$784$	−7.11974	−	5.97417i	−0.254277	−	0.213363i
$785$		0			0
$786$	14.1796	+	24.5598i	0.505770	+	0.876019i
$787$	23.3860	+	13.5019i	0.833622	+	0.481292i	0.855091	−	0.518478i	$-0.173501\pi$
$787$	23.3860	+	13.5019i	0.833622	+	0.481292i	−0.0214692	+	0.999770i	$0.506834\pi$
$788$	−0.371606	+	1.02098i	−0.0132379	+	0.0363709i
$789$	40.2631	+	14.6546i	1.43340	+	0.521716i
$790$		0			0
$791$	15.8645	+	27.4781i	0.564076	+	0.977009i
$792$	−22.2487	+	3.92304i	−0.790572	+	0.139399i
$793$	16.0028	−	19.0714i	0.568275	−	0.677244i
$794$	8.77457	−	7.36274i	0.311398	−	0.261294i
$795$		0			0
$796$	1.22137	−	0.444543i	0.0432904	−	0.0157564i
$797$			19.8667i			0.703715i	0.936054	+	0.351857i	$0.114450\pi$
$797$			19.8667i			0.703715i	−0.936054	+	0.351857i	$0.885550\pi$
$798$	−32.2328	+	39.3185i	−1.14103	+	1.39186i
$799$	16.1900			0.572762
$800$		0			0
$801$	10.5197	−	59.6601i	0.371695	−	2.10798i
$802$	3.19354	+	3.80592i	0.112768	+	0.134392i
$803$	5.35224	−	6.37855i	0.188876	−	0.225094i
$804$	−5.52078	−	31.3099i	−0.194703	−	1.10421i
$805$		0			0
$806$	−7.51307	+	13.0130i	−0.264637	+	0.458364i
$807$	2.77314	−	7.61915i	0.0976193	−	0.268207i
$808$	−4.86320	+	13.3615i	−0.171087	+	0.470057i
$809$	−9.17170	+	15.8859i	−0.322460	+	0.558517i	−0.980995	−	0.194033i	$-0.937843\pi$
$809$	−9.17170	+	15.8859i	−0.322460	+	0.558517i	0.658535	+	0.752550i	$0.271176\pi$
$810$		0			0
$811$	7.96210	+	45.1553i	0.279587	+	1.58562i	0.724003	+	0.689796i	$0.242300\pi$
$811$	7.96210	+	45.1553i	0.279587	+	1.58562i	−0.444416	+	0.895820i	$0.646589\pi$
$812$	13.7334	−	16.3669i	0.481950	−	0.574365i
$813$	15.2487	+	18.1727i	0.534795	+	0.637344i
$814$	6.39183	−	36.2499i	0.224034	−	1.27056i
$815$		0			0
$816$	−4.42655			−0.154960
$817$	−8.67269	−	4.87574i	−0.303419	−	0.170581i
$818$			1.29844i			0.0453989i
$819$	−112.127	+	40.8110i	−3.91805	+	1.42605i
$820$		0			0
$821$	−12.8300	+	10.7656i	−0.447769	+	0.375723i	−0.838607	−	0.544737i	$-0.816630\pi$
$821$	−12.8300	+	10.7656i	−0.447769	+	0.375723i	0.390838	+	0.920459i	$0.372185\pi$
$822$	6.06869	−	7.23239i	0.211670	−	0.252258i
$823$	−14.3394	+	2.52843i	−0.499841	+	0.0881355i	−0.417884	−	0.908500i	$-0.637228\pi$
$823$	−14.3394	+	2.52843i	−0.499841	+	0.0881355i	−0.0819572	+	0.996636i	$0.526117\pi$
$824$	4.00440	+	6.93582i	0.139500	+	0.241621i
$825$		0			0
$826$	−39.9809	−	14.5519i	−1.39111	−	0.506324i
$827$	−1.27214	+	3.49518i	−0.0442367	+	0.121539i	−0.959844	−	0.280535i	$-0.909488\pi$
$827$	−1.27214	+	3.49518i	−0.0442367	+	0.121539i	0.915607	+	0.402074i	$0.131710\pi$
$828$	−27.6378	−	15.9567i	−0.960481	−	0.554534i
$829$	−9.26652	−	16.0501i	−0.321840	−	0.557442i	0.659028	−	0.752118i	$-0.270968\pi$
$829$	−9.26652	−	16.0501i	−0.321840	−	0.557442i	−0.980868	+	0.194676i	$0.937634\pi$
$830$		0			0
$831$	44.6206	+	37.4411i	1.54787	+	1.29882i
$832$	−3.55196	−	4.23306i	−0.123142	−	0.146755i
$833$	−14.0216	−	2.47239i	−0.485820	−	0.0856633i
$834$	4.29708	−	1.56401i	0.148796	−	0.0541572i
$835$		0			0
$836$	−17.2252	+	6.49360i	−0.595747	+	0.224586i
$837$		−	18.4605i		−	0.638087i
$838$	12.3619	+	33.9641i	0.427035	+	1.17327i
$839$	−4.49001	+	25.4641i	−0.155013	+	0.879120i	0.803762	+	0.594951i	$0.202829\pi$
$839$	−4.49001	+	25.4641i	−0.155013	+	0.879120i	−0.958774	+	0.284168i	$0.908282\pi$
$840$		0			0
$841$	−0.754479	−	0.633083i	−0.0260165	−	0.0218305i
$842$	−29.9955	+	5.28902i	−1.03371	+	0.182272i
$843$	12.4161	−	7.16843i	0.427633	−	0.246894i
$844$	2.59008	−	4.48615i	0.0891543	−	0.154420i
$845$		0			0
$846$	−53.1259	−	19.3362i	−1.82650	−	0.664793i
$847$	−23.8957	−	13.7962i	−0.821066	−	0.474042i
$848$	2.23836	−	1.29232i	0.0768656	−	0.0443784i
$849$	−7.57812	−	42.9777i	−0.260080	−	1.47499i
$850$		0			0
$851$	39.8318	−	33.4229i	1.36542	−	1.14572i
$852$	21.2999	+	3.75575i	0.729723	+	0.128670i
$853$	−10.7040	−	29.4089i	−0.366497	−	1.00694i	−0.976683	−	0.214685i	$-0.931128\pi$
$853$	−10.7040	−	29.4089i	−0.366497	−	1.00694i	0.610186	−	0.792258i	$-0.291095\pi$
$854$	−18.1863			−0.622321
$855$		0			0
$856$	−17.5490			−0.599814
$857$	−1.15540	−	3.17443i	−0.0394677	−	0.108437i	0.918393	−	0.395669i	$-0.129487\pi$
$857$	−1.15540	−	3.17443i	−0.0394677	−	0.108437i	−0.957861	+	0.287232i	$0.907265\pi$
$858$	−66.4085	−	11.7096i	−2.26715	−	0.399760i
$859$	39.0805	−	32.7924i	1.33341	−	1.11886i	0.350142	−	0.936697i	$-0.386133\pi$
$859$	39.0805	−	32.7924i	1.33341	−	1.11886i	0.983268	−	0.182167i	$-0.0583112\pi$
$860$		0			0
$861$	6.53245	+	37.0474i	0.222625	+	1.26257i
$862$	31.2017	−	18.0143i	1.06273	−	0.613570i
$863$	21.3865	+	12.3475i	0.728006	+	0.420315i	0.817692	−	0.575656i	$-0.195253\pi$
$863$	21.3865	+	12.3475i	0.728006	+	0.420315i	−0.0896861	+	0.995970i	$0.528586\pi$
$864$	6.37942	+	2.32192i	0.217032	+	0.0789933i
$865$		0			0
$866$	−14.5606	+	25.2198i	−0.494791	+	0.857003i
$867$	36.6685	−	21.1705i	1.24533	−	0.718989i
$868$	10.8097	−	1.90605i	0.366906	−	0.0646954i
$869$	40.2388	+	33.7643i	1.36501	+	1.14538i
$870$		0			0
$871$	10.5578	−	59.8760i	0.357736	−	2.02882i
$872$	2.73090	+	7.50308i	0.0924798	+	0.254086i
$873$			73.0115i			2.47107i
$874$	−24.5360	−	8.61376i	−0.829941	−	0.291365i
$875$		0			0
$876$	−5.35352	+	1.94852i	−0.180879	+	0.0658345i
$877$	−6.87335	−	1.21196i	−0.232096	−	0.0409249i	0.0563901	−	0.998409i	$-0.482041\pi$
$877$	−6.87335	−	1.21196i	−0.232096	−	0.0409249i	−0.288487	+	0.957484i	$0.593152\pi$
$878$	2.09756	+	2.49978i	0.0707894	+	0.0843635i
$879$	−6.01371	−	5.04610i	−0.202837	−	0.170201i
$880$		0			0
$881$	−0.780822	−	1.35242i	−0.0263065	−	0.0455643i	0.852572	−	0.522609i	$-0.175041\pi$
$881$	−0.780822	−	1.35242i	−0.0263065	−	0.0455643i	−0.878879	+	0.477045i	$0.841708\pi$
$882$	43.0576	+	24.8593i	1.44983	+	0.837058i
$883$	−18.4078	+	50.5749i	−0.619471	+	1.70198i	0.0888076	+	0.996049i	$0.471694\pi$
$883$	−18.4078	+	50.5749i	−0.619471	+	1.70198i	−0.708278	+	0.705933i	$0.750528\pi$
$884$	−7.95468	−	2.89527i	−0.267545	−	0.0973783i
$885$		0			0
$886$	17.0395	+	29.5132i	0.572452	+	0.991516i
$887$	−49.2169	+	8.67826i	−1.65254	+	0.291388i	−0.920753	−	0.390145i	$-0.872425\pi$
$887$	−49.2169	+	8.67826i	−1.65254	+	0.291388i	−0.731787	+	0.681533i	$0.761314\pi$
$888$	−16.1886	+	19.2928i	−0.543253	+	0.647424i
$889$	57.3665	−	48.1362i	1.92401	−	1.61444i
$890$		0			0
$891$	14.1608	−	5.15412i	0.474405	−	0.172669i
$892$		−	8.08863i		−	0.270827i
$893$	−45.4555	−	7.47985i	−1.52111	−	0.250304i
$894$	34.8700			1.16623
$895$		0			0
$896$	−0.700949	+	3.97528i	−0.0234171	+	0.132805i
$897$	−61.2295	−	72.9705i	−2.04439	−	2.43641i
$898$	−20.6442	+	24.6028i	−0.688907	+	0.821007i
$899$	2.49927	+	14.1741i	0.0833553	+	0.472732i
$900$		0			0
$901$	1.97973	−	3.42899i	0.0659543	−	0.114236i
$902$	−4.65860	+	12.7994i	−0.155115	+	0.426174i
$903$	−9.10567	+	25.0176i	−0.303018	+	0.832535i
$904$	3.93016	−	6.80723i	0.130715	−	0.226405i
$905$		0			0
$906$	2.50106	+	14.1842i	0.0830923	+	0.471240i
$907$	−32.7593	+	39.0410i	−1.08776	+	1.29634i	−0.135586	+	0.990766i	$0.543292\pi$
$907$	−32.7593	+	39.0410i	−1.08776	+	1.29634i	−0.952169	+	0.305571i	$0.901153\pi$
$908$	4.20014	+	5.00554i	0.139387	+	0.166115i
$909$	13.2084	−	74.9085i	0.438095	−	2.48456i
$910$		0			0
$911$	−36.8444			−1.22071			−0.610355	−	0.792128i	$-0.708973\pi$
$911$	−36.8444			−1.22071			−0.610355	+	0.792128i	$0.708973\pi$
$912$	12.4281	+	2.04508i	0.411535	+	0.0677195i
$913$		−	16.2074i		−	0.536388i
$914$	8.14262	−	2.96367i	0.269334	−	0.0980295i
$915$		0			0
$916$	19.8326	−	16.6415i	0.655288	−	0.549852i
$917$	25.4653	−	30.3483i	0.840938	−	1.00219i
$918$	10.2420	−	1.80594i	0.338035	−	0.0596048i
$919$	−7.33804	−	12.7099i	−0.242060	−	0.419260i	0.719241	−	0.694761i	$-0.244490\pi$
$919$	−7.33804	−	12.7099i	−0.242060	−	0.419260i	−0.961301	+	0.275501i	$0.911156\pi$
$920$		0			0
$921$	68.8363	+	25.0543i	2.26823	+	0.825569i
$922$	6.06724	−	16.6696i	0.199814	−	0.548984i
$923$	35.8202	+	20.6808i	1.17904	+	0.680717i
$924$	24.6296	+	42.6598i	0.810256	+	1.40340i
$925$		0			0
$926$	−20.3013	−	17.0348i	−0.667143	−	0.559799i
$927$	−27.5387	−	32.8194i	−0.904490	−	1.07793i
$928$	−5.21252	−	0.919107i	−0.171109	−	0.0301712i
$929$	35.9586	−	13.0879i	1.17976	−	0.429399i	0.323645	−	0.946178i	$-0.395092\pi$
$929$	35.9586	−	13.0879i	1.17976	−	0.429399i	0.856119	+	0.516780i	$0.172869\pi$
$930$		0			0
$931$	38.2252	+	13.4196i	1.25278	+	0.439809i
$932$			22.7007i			0.743587i
$933$	−3.71039	−	10.1942i	−0.121473	−	0.333744i
$934$	−2.72884	+	15.4760i	−0.0892905	+	0.506392i
$935$		0			0
$936$	22.6445	+	19.0010i	0.740160	+	0.621068i
$937$	9.32123	−	1.64359i	0.304511	−	0.0536936i	−0.0193046	−	0.999814i	$-0.506145\pi$
$937$	9.32123	−	1.64359i	0.304511	−	0.0536936i	0.323816	+	0.946120i	$0.395034\pi$
$938$	−38.4634	+	22.2069i	−1.25587	+	0.725079i
$939$	−30.8630	+	53.4562i	−1.00717	+	1.74448i
$940$		0			0
$941$	−21.1763	−	7.70755i	−0.690328	−	0.251259i	−0.0270523	−	0.999634i	$-0.508612\pi$
$941$	−21.1763	−	7.70755i	−0.690328	−	0.251259i	−0.663276	+	0.748375i	$0.730834\pi$
$942$	−39.2152	−	22.6409i	−1.27770	−	0.737680i
$943$	−16.6631	+	9.62044i	−0.542625	+	0.313285i
$944$	1.83030	+	10.3801i	0.0595710	+	0.337844i
$945$		0			0
$946$	−7.38435	+	6.19621i	−0.240086	+	0.201456i
$947$	−40.7294	−	7.18168i	−1.32353	−	0.233373i	−0.533163	−	0.846012i	$-0.678997\pi$
$947$	−40.7294	−	7.18168i	−1.32353	−	0.233373i	−0.790363	+	0.612639i	$0.790108\pi$
$948$	−12.2922	−	33.7724i	−0.399231	−	1.09688i
$949$	−10.8950			−0.353665
$950$		0			0
$951$	59.2764			1.92217
$952$	2.11497	+	5.81083i	0.0685466	+	0.188330i
$953$	−1.63331	−	0.287997i	−0.0529083	−	0.00932915i	0.147131	−	0.989117i	$-0.452996\pi$
$953$	−1.63331	−	0.287997i	−0.0529083	−	0.00932915i	−0.200040	+	0.979788i	$0.564107\pi$
$954$	−10.5916	+	8.88743i	−0.342916	+	0.287741i
$955$		0			0
$956$	−1.55547	−	8.82152i	−0.0503076	−	0.285308i
$957$	−55.9370	+	32.2952i	−1.80819	+	1.04396i
$958$	7.94808	+	4.58883i	0.256791	+	0.148258i
$959$	−12.3937	−	4.51093i	−0.400213	−	0.145666i
$960$		0			0
$961$	11.8029	−	20.4432i	0.380738	−	0.659457i
$962$	−41.7103	+	24.0814i	−1.34479	+	0.776416i
$963$	92.4516	−	16.3017i	2.97921	−	0.525315i
$964$	−2.56969	−	2.15623i	−0.0827642	−	0.0694474i
$965$		0			0
$966$	−12.0831	+	68.5268i	−0.388768	+	2.20481i
$967$	−13.8597	−	38.0792i	−0.445697	−	1.22454i	−0.935692	−	0.352818i	$-0.885223\pi$
$967$	−13.8597	−	38.0792i	−0.445697	−	1.22454i	0.489994	−	0.871726i	$-0.336999\pi$
$968$			6.83554i			0.219703i
$969$	18.0546	−	6.80625i	0.579997	−	0.218648i
$970$		0			0
$971$	28.2395	−	10.2783i	0.906248	−	0.329847i	0.153494	−	0.988150i	$-0.450947\pi$
$971$	28.2395	−	10.2783i	0.906248	−	0.329847i	0.752754	+	0.658302i	$0.228725\pi$
$972$	9.90305	+	1.74617i	0.317640	+	0.0560086i
$973$	−4.10622	−	4.89360i	−0.131639	−	0.156882i
$974$	20.3715	+	17.0937i	0.652745	+	0.547718i
$975$		0			0
$976$	2.25267	+	3.90174i	0.0721061	+	0.124892i
$977$	26.0144	+	15.0194i	0.832273	+	0.480513i	0.854630	−	0.519237i	$-0.173784\pi$
$977$	26.0144	+	15.0194i	0.832273	+	0.480513i	−0.0223570	+	0.999750i	$0.507117\pi$
$978$	−8.31408	+	22.8427i	−0.265855	+	0.730431i
$979$	−44.9419	−	16.3575i	−1.43635	−	0.522789i
$980$		0			0
$981$	−21.3566	−	36.9908i	−0.681865	−	1.18102i
$982$	−33.4038	+	5.89000i	−1.06596	+	0.187957i
$983$	12.4389	−	14.8241i	0.396740	−	0.472816i	−0.530283	−	0.847821i	$-0.677914\pi$
$983$	12.4389	−	14.8241i	0.396740	−	0.472816i	0.927023	+	0.375004i	$0.122359\pi$
$984$	7.13911	−	5.99042i	0.227586	−	0.190968i
$985$		0			0
$986$	−7.61936	+	2.77322i	−0.242650	+	0.0883173i
$987$			123.270i			3.92371i
$988$	20.9961	+	11.8039i	0.667975	+	0.375532i
$989$	−13.6169			−0.432993
$990$		0			0
$991$	3.11302	−	17.6548i	0.0988885	−	0.560824i	−0.894598	−	0.446872i	$-0.852538\pi$
$991$	3.11302	−	17.6548i	0.0988885	−	0.560824i	0.993486	−	0.113952i	$-0.0363510\pi$
$992$	−1.74789	−	2.08306i	−0.0554956	−	0.0661371i
$993$	−60.8239	+	72.4871i	−1.93019	+	2.30031i
$994$	−5.24667	−	29.7553i	−0.166414	−	0.943782i
$995$		0			0
$996$	−5.54460	+	9.60353i	−0.175687	+	0.304299i
$997$	14.1528	−	38.8845i	0.448224	−	1.23149i	−0.485735	−	0.874106i	$-0.661448\pi$
$997$	14.1528	−	38.8845i	0.448224	−	1.23149i	0.933959	−	0.357380i	$-0.116330\pi$
$998$	−9.45462	+	25.9763i	−0.299281	+	0.822267i
$999$	29.5854	−	51.2434i	0.936041	−	1.62127i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.u.h.499.8		48
5.2	odd	4		950.2.l.k.651.4	yes	24
5.3	odd	4		950.2.l.j.651.1	yes	24
5.4	even	2	inner	950.2.u.h.499.1		48
19.4	even	9	inner	950.2.u.h.99.1		48
95.4	even	18	inner	950.2.u.h.99.8		48
95.23	odd	36		950.2.l.j.251.1	✓	24
95.42	odd	36		950.2.l.k.251.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.l.j.251.1	✓	24	95.23	odd	36
950.2.l.j.651.1	yes	24	5.3	odd	4
950.2.l.k.251.4	yes	24	95.42	odd	36
950.2.l.k.651.4	yes	24	5.2	odd	4
950.2.u.h.99.1		48	19.4	even	9	inner
950.2.u.h.99.8		48	95.4	even	18	inner
950.2.u.h.499.1		48	5.4	even	2	inner
950.2.u.h.499.8		48	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.342020 + 0.939693i) q^{2} +(2.84564 + 0.501764i) q^{3} +(-0.766044 + 0.642788i) q^{4} +(0.501764 + 2.84564i) q^{6} +(3.49580 - 2.01830i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(5.02684 + 1.82962i) q^{9} +O(q^{10})\)	\(q+(0.342020 + 0.939693i) q^{2} +(2.84564 + 0.501764i) q^{3} +(-0.766044 + 0.642788i) q^{4} +(0.501764 + 2.84564i) q^{6} +(3.49580 - 2.01830i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(5.02684 + 1.82962i) q^{9} +(2.11161 - 3.65741i) q^{11} +(-2.50242 + 1.44477i) q^{12} +(-5.44192 + 0.959556i) q^{13} +(3.09222 + 2.59468i) q^{14} +(0.173648 - 0.984808i) q^{16} +(-0.523948 - 1.43954i) q^{17} +5.34945i q^{18} +(0.805977 + 4.28374i) q^{19} +(10.9605 - 3.98930i) q^{21} +(4.15905 + 0.733353i) q^{22} +(3.83470 + 4.57002i) q^{23} +(-2.21352 - 1.85736i) q^{24} +(-2.76293 - 4.78554i) q^{26} +(5.87931 + 3.39442i) q^{27} +(-1.38060 + 3.79317i) q^{28} +(-4.97373 - 1.81029i) q^{29} +(-1.35962 - 2.35493i) q^{31} +(0.984808 - 0.173648i) q^{32} +(7.84404 - 9.34816i) q^{33} +(1.17352 - 0.984700i) q^{34} +(-5.02684 + 1.82962i) q^{36} -8.71589i q^{37} +(-3.74974 + 2.22249i) q^{38} -15.9672 q^{39} +(-0.560056 + 3.17623i) q^{41} +(7.49743 + 8.93509i) q^{42} +(-1.46718 + 1.74851i) q^{43} +(0.733353 + 4.15905i) q^{44} +(-2.98287 + 5.16648i) q^{46} +(-3.61462 + 9.93108i) q^{47} +(0.988282 - 2.71528i) q^{48} +(4.64708 - 8.04898i) q^{49} +(-0.768663 - 4.35930i) q^{51} +(3.55196 - 4.23306i) q^{52} +(1.66137 + 1.97995i) q^{53} +(-1.17887 + 6.68570i) q^{54} -4.03660 q^{56} +(0.144099 + 12.5944i) q^{57} -5.29293i q^{58} +(-9.90460 + 3.60498i) q^{59} +(-3.45129 + 2.89597i) q^{61} +(1.74789 - 2.08306i) q^{62} +(21.2656 - 3.74969i) q^{63} +(0.500000 + 0.866025i) q^{64} +(11.4672 + 4.17372i) q^{66} +(-3.76316 + 10.3392i) q^{67} +(1.32668 + 0.765961i) q^{68} +(8.61912 + 14.9288i) q^{69} +(-5.73392 - 4.81133i) q^{71} +(-3.43856 - 4.09792i) q^{72} +(1.94167 + 0.342370i) q^{73} +(8.19026 - 2.98101i) q^{74} +(-3.37095 - 2.76346i) q^{76} -17.0474i q^{77} +(-5.46111 - 15.0043i) q^{78} +(-2.15982 + 12.2490i) q^{79} +(2.73346 + 2.29365i) q^{81} +(-3.17623 + 0.560056i) q^{82} +(3.32355 - 1.91885i) q^{83} +(-5.83197 + 10.1013i) q^{84} +(-2.14487 - 0.780669i) q^{86} +(-13.2451 - 7.64707i) q^{87} +(-3.65741 + 2.11161i) q^{88} +(-1.96650 - 11.1526i) q^{89} +(-17.0872 + 14.3378i) q^{91} +(-5.87510 - 1.03594i) q^{92} +(-2.68737 - 7.38349i) q^{93} -10.5684 q^{94} +2.88954 q^{96} +(4.66803 + 12.8253i) q^{97} +(9.15296 + 1.61391i) q^{98} +(17.3064 - 14.5218i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 12 q^{11} + 30 q^{14} + 30 q^{19} - 36 q^{21} - 18 q^{26} + 24 q^{29} + 18 q^{31} + 18 q^{34} - 132 q^{39} + 36 q^{41} - 6 q^{46} + 54 q^{49} - 6 q^{51} - 54 q^{54} - 12 q^{56} - 72 q^{59} + 24 q^{61} + 24 q^{64} + 96 q^{66} - 42 q^{69} - 78 q^{71} - 36 q^{74} + 12 q^{76} + 84 q^{79} - 72 q^{81} - 18 q^{84} - 78 q^{86} + 72 q^{89} + 24 q^{91} - 24 q^{94} + 12 q^{96} - 102 q^{99}+O(q^{100}) \) 48 * q - 12 * q^11 + 30 * q^14 + 30 * q^19 - 36 * q^21 - 18 * q^26 + 24 * q^29 + 18 * q^31 + 18 * q^34 - 132 * q^39 + 36 * q^41 - 6 * q^46 + 54 * q^49 - 6 * q^51 - 54 * q^54 - 12 * q^56 - 72 * q^59 + 24 * q^61 + 24 * q^64 + 96 * q^66 - 42 * q^69 - 78 * q^71 - 36 * q^74 + 12 * q^76 + 84 * q^79 - 72 * q^81 - 18 * q^84 - 78 * q^86 + 72 * q^89 + 24 * q^91 - 24 * q^94 + 12 * q^96 - 102 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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