LMFDB - Embedded newform 121.4.c.d.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [121,4,Mod(3,121)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(121, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("121.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 121 = 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	121.c (of order $5$, degree $4$, 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:	$7.13923111069$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.324000000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 $ x^8 + 3x^6 + 9x^4 + 27*x^2 + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			3.1
Root			$-0.535233 - 1.64728i$ of defining polynomial
Character	$\chi$	$=$	121.3
Dual form			121.4.c.d.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.61153 + 2.62393i) q^{2} +(-2.30653 - 7.09878i) q^{3} +(3.68602 - 11.3444i) q^{4} +(6.84760 + 4.97507i) q^{5} +(26.9569 + 19.5853i) q^{6} +(-6.25720 + 19.2577i) q^{7} +(5.41889 + 16.6776i) q^{8} +(-23.2292 + 16.8770i) q^{9} -37.7846 q^{10} -89.0333 q^{12} +(49.7836 - 36.1699i) q^{13} +(-27.9328 - 85.9682i) q^{14} +(19.5227 - 60.0848i) q^{15} +(13.8695 + 10.0768i) q^{16} +(-56.1084 - 40.7652i) q^{17} +(39.6088 - 121.903i) q^{18} +(-2.21779 - 6.82565i) q^{19} +(81.6796 - 59.3437i) q^{20} +151.138 q^{21} +50.3154 q^{23} +(105.892 - 76.9351i) q^{24} +(-16.4888 - 50.7474i) q^{25} +(-84.8877 + 261.258i) q^{26} +(10.3430 + 7.51461i) q^{27} +(195.402 + 141.968i) q^{28} +(44.2425 - 136.164i) q^{29} +(87.1515 + 268.225i) q^{30} +(206.148 - 149.775i) q^{31} -216.818 q^{32} +309.603 q^{34} +(-138.655 + 100.739i) q^{35} +(105.836 + 325.730i) q^{36} +(104.035 - 320.187i) q^{37} +(25.9197 + 18.8317i) q^{38} +(-371.590 - 269.976i) q^{39} +(-45.8660 + 141.161i) q^{40} +(-55.0272 - 169.356i) q^{41} +(-545.842 + 396.577i) q^{42} +55.7898 q^{43} -243.028 q^{45} +(-181.716 + 132.024i) q^{46} +(-79.2676 - 243.961i) q^{47} +(39.5423 - 121.699i) q^{48} +(-54.2125 - 39.3877i) q^{49} +(192.708 + 140.010i) q^{50} +(-159.967 + 492.328i) q^{51} +(-226.822 - 698.088i) q^{52} +(-172.684 + 125.462i) q^{53} -57.0718 q^{54} -355.079 q^{56} +(-43.3384 + 31.4872i) q^{57} +(197.503 + 607.852i) q^{58} +(-246.439 + 758.460i) q^{59} +(-609.665 - 442.947i) q^{60} +(136.479 + 99.1578i) q^{61} +(-351.510 + 1081.84i) q^{62} +(-179.662 - 552.942i) q^{63} +(672.090 - 488.302i) q^{64} +520.846 q^{65} -366.105 q^{67} +(-669.273 + 486.255i) q^{68} +(-116.054 - 357.178i) q^{69} +(236.426 - 727.644i) q^{70} +(632.643 + 459.642i) q^{71} +(-407.344 - 295.953i) q^{72} +(295.896 - 910.673i) q^{73} +(464.422 + 1429.35i) q^{74} +(-322.213 + 234.101i) q^{75} -85.6077 q^{76} +2050.41 q^{78} +(473.750 - 344.199i) q^{79} +(44.8399 + 138.003i) q^{80} +(-210.076 + 646.548i) q^{81} +(643.112 + 467.248i) q^{82} +(-531.257 - 385.980i) q^{83} +(557.099 - 1714.57i) q^{84} +(-181.398 - 558.287i) q^{85} +(-201.487 + 146.389i) q^{86} -1068.65 q^{87} +72.6819 q^{89} +(877.705 - 637.690i) q^{90} +(385.042 + 1185.04i) q^{91} +(185.463 - 570.797i) q^{92} +(-1538.71 - 1117.94i) q^{93} +(926.414 + 673.079i) q^{94} +(18.7716 - 57.7730i) q^{95} +(500.098 + 1539.14i) q^{96} +(792.513 - 575.794i) q^{97} +299.141 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 8 q^{3} - 10 q^{4} + 10 q^{5} + 32 q^{6} - 8 q^{7} - 42 q^{8} - 2 q^{9} - 136 q^{10} - 352 q^{12} + 130 q^{13} + 160 q^{14} - 64 q^{15} + 62 q^{16} - 14 q^{17} - 194 q^{18} - 48 q^{19} + 98 q^{20}+ \cdots - 3288 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 + 8 * q^3 - 10 * q^4 + 10 * q^5 + 32 * q^6 - 8 * q^7 - 42 * q^8 - 2 * q^9 - 136 * q^10 - 352 * q^12 + 130 * q^13 + 160 * q^14 - 64 * q^15 + 62 * q^16 - 14 * q^17 - 194 * q^18 - 48 * q^19 + 98 * q^20 + 544 * q^21 - 512 * q^23 + 144 * q^24 + 176 * q^25 + 106 * q^26 - 16 * q^27 + 296 * q^28 - 30 * q^29 - 280 * q^30 + 184 * q^31 - 1208 * q^32 + 1784 * q^34 - 128 * q^35 - 394 * q^36 - 126 * q^37 + 168 * q^38 - 496 * q^39 + 186 * q^40 + 370 * q^41 - 712 * q^42 + 1056 * q^43 - 808 * q^45 - 664 * q^46 - 256 * q^47 - 152 * q^48 - 522 * q^49 - 64 * q^50 + 488 * q^51 + 602 * q^52 + 162 * q^53 - 512 * q^54 + 1344 * q^56 - 24 * q^57 - 918 * q^58 + 1304 * q^59 - 752 * q^60 - 300 * q^61 + 1312 * q^62 + 1336 * q^63 + 262 * q^64 + 2504 * q^65 - 2624 * q^67 - 934 * q^68 + 280 * q^69 - 872 * q^70 + 1176 * q^71 + 150 * q^72 - 668 * q^73 - 2022 * q^74 - 464 * q^75 - 768 * q^76 + 7840 * q^78 + 416 * q^79 - 214 * q^80 - 26 * q^81 + 322 * q^82 - 960 * q^83 - 1832 * q^84 + 502 * q^85 + 264 * q^86 - 4032 * q^87 - 4296 * q^89 + 1186 * q^90 + 688 * q^91 - 944 * q^92 - 1864 * q^93 + 2408 * q^94 + 24 * q^95 - 1664 * q^96 + 338 * q^97 - 3288 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/121\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−3.61153	+	2.62393i	−1.27687	+	0.927700i	−0.999454	−	0.0330493i	$-0.989478\pi$
$2$	−3.61153	+	2.62393i	−1.27687	+	0.927700i	−0.277416	+	0.960750i	$0.589478\pi$
$3$	−2.30653	−	7.09878i	−0.443893	−	1.36616i	−0.883694	−	0.468066i	$-0.844951\pi$
$3$	−2.30653	−	7.09878i	−0.443893	−	1.36616i	0.439801	−	0.898095i	$-0.355049\pi$
$4$	3.68602	−	11.3444i	0.460752	−	1.41805i
$5$	6.84760	+	4.97507i	0.612468	+	0.444984i	0.850283	−	0.526326i	$-0.176431\pi$
$5$	6.84760	+	4.97507i	0.612468	+	0.444984i	−0.237814	+	0.971311i	$0.576431\pi$
$6$	26.9569	+	19.5853i	1.83418	+	1.33261i
$7$	−6.25720	+	19.2577i	−0.337857	+	1.03982i	0.627441	+	0.778664i	$0.284102\pi$
$7$	−6.25720	+	19.2577i	−0.337857	+	1.03982i	−0.965298	+	0.261152i	$0.915898\pi$
$8$	5.41889	+	16.6776i	0.239483	+	0.737054i
$9$	−23.2292	+	16.8770i	−0.860339	+	0.625073i
$10$	−37.7846			−1.19485
$11$		0			0
$11$		0			0
$12$	−89.0333			−2.14181
$13$	49.7836	−	36.1699i	1.06211	−	0.771671i	0.0876357	−	0.996153i	$-0.472069\pi$
$13$	49.7836	−	36.1699i	1.06211	−	0.771671i	0.974478	+	0.224482i	$0.0720689\pi$
$14$	−27.9328	−	85.9682i	−0.533239	−	1.64114i
$15$	19.5227	−	60.0848i	0.336050	−	1.03426i
$16$	13.8695	+	10.0768i	0.216710	+	0.157449i
$17$	−56.1084	−	40.7652i	−0.800488	−	0.581588i	0.110569	−	0.993868i	$-0.464733\pi$
$17$	−56.1084	−	40.7652i	−0.800488	−	0.581588i	−0.911057	+	0.412280i	$0.864733\pi$
$18$	39.6088	−	121.903i	0.518661	−	1.59627i
$19$	−2.21779	−	6.82565i	−0.0267787	−	0.0824164i	0.936774	−	0.349935i	$-0.113796\pi$
$19$	−2.21779	−	6.82565i	−0.0267787	−	0.0824164i	−0.963553	+	0.267519i	$0.913796\pi$
$20$	81.6796	−	59.3437i	0.913206	−	0.663483i
$21$	151.138			1.57053
$22$		0			0
$23$	50.3154			0.456151			0.228076	−	0.973643i	$-0.426757\pi$
$23$	50.3154			0.456151			0.228076	+	0.973643i	$0.426757\pi$
$24$	105.892	−	76.9351i	0.900630	−	0.654346i
$25$	−16.4888	−	50.7474i	−0.131911	−	0.405979i
$26$	−84.8877	+	261.258i	−0.640302	+	1.97065i
$27$	10.3430	+	7.51461i	0.0737224	+	0.0535625i
$28$	195.402	+	141.968i	1.31884	+	0.958195i
$29$	44.2425	−	136.164i	0.283297	−	0.871900i	−0.703606	−	0.710590i	$-0.748428\pi$
$29$	44.2425	−	136.164i	0.283297	−	0.871900i	0.986904	−	0.161310i	$-0.0515719\pi$
$30$	87.1515	+	268.225i	0.530387	+	1.63236i
$31$	206.148	−	149.775i	1.19436	−	0.867755i	0.200644	−	0.979664i	$-0.435696\pi$
$31$	206.148	−	149.775i	1.19436	−	0.867755i	0.993718	+	0.111909i	$0.0356964\pi$
$32$	−216.818			−1.19776
$33$		0			0
$34$	309.603			1.56166
$35$	−138.655	+	100.739i	−0.669628	+	0.486513i
$36$	105.836	+	325.730i	0.489981	+	1.50801i
$37$	104.035	−	320.187i	0.462250	−	1.42266i	−0.400159	−	0.916446i	$-0.631045\pi$
$37$	104.035	−	320.187i	0.462250	−	1.42266i	0.862409	−	0.506212i	$-0.168955\pi$
$38$	25.9197	+	18.8317i	0.110651	+	0.0803924i
$39$	−371.590	−	269.976i	−1.52569	−	1.10848i
$40$	−45.8660	+	141.161i	−0.181301	+	0.557988i
$41$	−55.0272	−	169.356i	−0.209605	−	0.645098i	−0.999493	−	0.0318465i	$-0.989861\pi$
$41$	−55.0272	−	169.356i	−0.209605	−	0.645098i	0.789888	−	0.613251i	$-0.210139\pi$
$42$	−545.842	+	396.577i	−2.00536	+	1.45698i
$43$	55.7898			0.197857			0.0989286	−	0.995095i	$-0.468458\pi$
$43$	55.7898			0.197857			0.0989286	+	0.995095i	$0.468458\pi$
$44$		0			0
$45$	−243.028			−0.805078
$46$	−181.716	+	132.024i	−0.582446	+	0.423172i
$47$	−79.2676	−	243.961i	−0.246008	−	0.757134i	−0.995469	−	0.0950859i	$-0.969687\pi$
$47$	−79.2676	−	243.961i	−0.246008	−	0.757134i	0.749461	−	0.662048i	$-0.230313\pi$
$48$	39.5423	−	121.699i	0.118905	−	0.365952i
$49$	−54.2125	−	39.3877i	−0.158054	−	0.114833i
$50$	192.708	+	140.010i	0.545060	+	0.396009i
$51$	−159.967	+	492.328i	−0.439213	+	1.35176i
$52$	−226.822	−	698.088i	−0.604896	−	1.86168i
$53$	−172.684	+	125.462i	−0.447546	+	0.325161i	−0.788626	−	0.614873i	$-0.789207\pi$
$53$	−172.684	+	125.462i	−0.447546	+	0.325161i	0.341080	+	0.940034i	$0.389207\pi$
$54$	−57.0718			−0.143824
$55$		0			0
$56$	−355.079			−0.847312
$57$	−43.3384	+	31.4872i	−0.100707	+	0.0731681i
$58$	197.503	+	607.852i	0.447128	+	1.37612i
$59$	−246.439	+	758.460i	−0.543790	+	1.67361i	0.180061	+	0.983655i	$0.442370\pi$
$59$	−246.439	+	758.460i	−0.543790	+	1.67361i	−0.723851	+	0.689957i	$0.757630\pi$
$60$	−609.665	−	442.947i	−1.31179	−	0.953071i
$61$	136.479	+	99.1578i	0.286465	+	0.208129i	0.721732	−	0.692172i	$-0.243346\pi$
$61$	136.479	+	99.1578i	0.286465	+	0.208129i	−0.435268	+	0.900301i	$0.643346\pi$
$62$	−351.510	+	1081.84i	−0.720029	+	2.21602i
$63$	−179.662	−	552.942i	−0.359290	−	1.10578i
$64$	672.090	−	488.302i	1.31268	−	0.953714i
$65$	520.846			0.993892
$66$		0			0
$67$	−366.105			−0.667565			−0.333783	−	0.942650i	$-0.608325\pi$
$67$	−366.105			−0.667565			−0.333783	+	0.942650i	$0.608325\pi$
$68$	−669.273	+	486.255i	−1.19355	+	0.867163i
$69$	−116.054	−	357.178i	−0.202482	−	0.623176i
$70$	236.426	−	727.644i	0.403690	−	1.24243i
$71$	632.643	+	459.642i	1.05748	+	0.768302i	0.973620	−	0.228175i	$-0.0732760\pi$
$71$	632.643	+	459.642i	1.05748	+	0.768302i	0.0838575	+	0.996478i	$0.473276\pi$
$72$	−407.344	−	295.953i	−0.666749	−	0.484422i
$73$	295.896	−	910.673i	0.474410	−	1.46009i	−0.372341	−	0.928096i	$-0.621445\pi$
$73$	295.896	−	910.673i	0.474410	−	1.46009i	0.846751	−	0.531989i	$-0.178555\pi$
$74$	464.422	+	1429.35i	0.729568	+	2.24538i
$75$	−322.213	+	234.101i	−0.496079	+	0.360422i
$76$	−85.6077			−0.129209
$77$		0			0
$78$	2050.41			2.97645
$79$	473.750	−	344.199i	0.674697	−	0.490196i	−0.196897	−	0.980424i	$-0.563087\pi$
$79$	473.750	−	344.199i	0.674697	−	0.490196i	0.871594	+	0.490228i	$0.163087\pi$
$80$	44.8399	+	138.003i	0.0626657	+	0.192865i
$81$	−210.076	+	646.548i	−0.288170	+	0.886896i
$82$	643.112	+	467.248i	0.866096	+	0.629256i
$83$	−531.257	−	385.980i	−0.702566	−	0.510444i	0.178201	−	0.983994i	$-0.442972\pi$
$83$	−531.257	−	385.980i	−0.702566	−	0.510444i	−0.880767	+	0.473550i	$0.842972\pi$
$84$	557.099	−	1714.57i	0.723625	−	2.22709i
$85$	−181.398	−	558.287i	−0.231476	−	0.712409i
$86$	−201.487	+	146.389i	−0.252638	+	0.183552i
$87$	−1068.65			−1.31691
$88$		0			0
$89$	72.6819			0.0865648			0.0432824	−	0.999063i	$-0.486218\pi$
$89$	72.6819			0.0865648			0.0432824	+	0.999063i	$0.486218\pi$
$90$	877.705	−	637.690i	1.02798	−	0.746871i
$91$	385.042	+	1185.04i	0.443554	+	1.36512i
$92$	185.463	−	570.797i	0.210173	−	0.646845i
$93$	−1538.71	−	1117.94i	−1.71566	−	1.24650i
$94$	926.414	+	673.079i	1.01651	+	0.738540i
$95$	18.7716	−	57.7730i	0.0202729	−	0.0623935i
$96$	500.098	+	1539.14i	0.531677	+	1.63633i
$97$	792.513	−	575.794i	0.829562	−	0.602712i	−0.0898736	−	0.995953i	$-0.528646\pi$
$97$	792.513	−	575.794i	0.829562	−	0.602712i	0.919435	+	0.393241i	$0.128646\pi$
$98$	299.141			0.308345
$99$		0			0
$100$	−636.477			−0.636477
$101$	828.782	−	602.145i	0.816504	−	0.593225i	−0.0992051	−	0.995067i	$-0.531630\pi$
$101$	828.782	−	602.145i	0.816504	−	0.593225i	0.915709	+	0.401842i	$0.131630\pi$
$102$	−714.109	−	2197.80i	−0.693209	−	2.13348i
$103$	−229.199	+	705.401i	−0.219258	+	0.674808i	0.779565	+	0.626321i	$0.215440\pi$
$103$	−229.199	+	705.401i	−0.219258	+	0.674808i	−0.998824	+	0.0484872i	$0.984560\pi$
$104$	873.000	+	634.272i	0.823122	+	0.598033i
$105$	1034.94	+	751.925i	0.961899	+	0.698861i
$106$	294.449	−	906.220i	0.269806	−	0.830376i
$107$	401.065	+	1234.35i	0.362359	+	1.11523i	0.951618	+	0.307283i	$0.0994198\pi$
$107$	401.065	+	1234.35i	0.362359	+	1.11523i	−0.589259	+	0.807944i	$0.700580\pi$
$108$	123.373	−	89.6357i	0.109922	−	0.0798630i
$109$	691.844			0.607951			0.303975	−	0.952680i	$-0.401686\pi$
$109$	691.844			0.607951			0.303975	+	0.952680i	$0.401686\pi$
$110$		0			0
$111$	−2512.89			−2.14877
$112$	−280.839	+	204.041i	−0.236935	+	0.172144i
$113$	−166.557	−	512.610i	−0.138658	−	0.426746i	0.857483	−	0.514512i	$-0.172027\pi$
$113$	−166.557	−	512.610i	−0.138658	−	0.426746i	−0.996141	+	0.0877666i	$0.972027\pi$
$114$	73.8978	−	227.434i	0.0607120	−	0.186852i
$115$	344.540	+	250.323i	0.279378	+	0.202980i
$116$	−1381.62	−	1003.81i	−1.10587	−	0.803460i
$117$	−545.992	+	1680.39i	−0.431428	+	1.32780i
$118$	−1100.13	−	3385.84i	−0.858262	−	2.64146i
$119$	1136.12	−	825.442i	0.875195	−	0.635867i
$120$	1107.86			0.842781
$121$		0			0
$122$	−753.082			−0.558859
$123$	−1075.30	+	781.252i	−0.788266	+	0.572709i
$124$	−939.244	−	2890.70i	−0.680215	−	2.09349i
$125$	466.507	−	1435.76i	0.333805	−	1.02735i
$126$	2099.74	+	1525.55i	1.48460	+	1.07862i
$127$	569.345	+	413.653i	0.397804	+	0.289022i	0.768646	−	0.639674i	$-0.220931\pi$
$127$	569.345	+	413.653i	0.397804	+	0.289022i	−0.370842	+	0.928696i	$0.620931\pi$
$128$	−610.000	+	1877.39i	−0.421226	+	1.29640i
$129$	−128.681	−	396.039i	−0.0878274	−	0.270305i
$130$	−1881.05	+	1366.67i	−1.26907	+	0.922034i
$131$	−446.318			−0.297672			−0.148836	−	0.988862i	$-0.547553\pi$
$131$	−446.318			−0.297672			−0.148836	+	0.988862i	$0.547553\pi$
$132$		0			0
$133$	145.323			0.0947453
$134$	1322.20	−	960.635i	0.852394	−	0.619300i
$135$	33.4388	+	102.914i	0.0213182	+	0.0656106i
$136$	375.821	−	1156.66i	0.236959	−	0.729284i
$137$	−1593.34	−	1157.63i	−0.993637	−	0.721919i	−0.0329221	−	0.999458i	$-0.510481\pi$
$137$	−1593.34	−	1157.63i	−0.993637	−	0.721919i	−0.960714	+	0.277539i	$0.910481\pi$
$138$	1356.34	+	985.441i	0.836664	+	0.607872i
$139$	79.9427	−	246.038i	0.0487817	−	0.150135i	−0.923698	−	0.383120i	$-0.874850\pi$
$139$	79.9427	−	246.038i	0.0487817	−	0.150135i	0.972480	+	0.232986i	$0.0748495\pi$
$140$	631.736	+	1944.28i	0.381367	+	1.17373i
$141$	−1548.99	+	1125.41i	−0.925166	+	0.672173i
$142$	−3490.88			−2.06302
$143$		0			0
$144$	−492.241			−0.284862
$145$	980.383	−	712.290i	0.561492	−	0.407948i
$146$	1320.91	+	4065.34i	0.748761	+	2.30445i
$147$	−154.562	+	475.692i	−0.0867213	+	0.266901i
$148$	−3248.85	−	2360.43i	−1.80442	−	1.31099i
$149$	−79.9537	−	58.0898i	−0.0439602	−	0.0319389i	0.565588	−	0.824688i	$-0.308649\pi$
$149$	−79.9537	−	58.0898i	−0.0439602	−	0.0319389i	−0.609548	+	0.792749i	$0.708649\pi$
$150$	549.416	−	1690.93i	0.299064	−	0.920425i
$151$	459.679	+	1414.75i	0.247736	+	0.762454i	0.995174	+	0.0981223i	$0.0312836\pi$
$151$	459.679	+	1414.75i	0.247736	+	0.762454i	−0.747438	+	0.664331i	$0.768716\pi$
$152$	101.818	−	73.9749i	0.0543323	−	0.0394747i
$153$	1991.34			1.05223
$154$		0			0
$155$	2156.76			1.11765
$156$	−4432.40	+	3220.33i	−2.27485	+	1.65277i
$157$	652.647	+	2008.64i	0.331764	+	1.02106i	0.968294	+	0.249812i	$0.0803689\pi$
$157$	652.647	+	2008.64i	0.331764	+	1.02106i	−0.636531	+	0.771251i	$0.719631\pi$
$158$	−807.808	+	2486.18i	−0.406745	+	1.25183i
$159$	1288.93	+	936.461i	0.642884	+	0.467083i
$160$	−1484.68	−	1078.69i	−0.733591	−	0.532985i
$161$	−314.833	+	968.956i	−0.154114	+	0.474313i
$162$	−937.801	−	2886.25i	−0.454818	−	1.39979i
$163$	−1120.47	+	814.069i	−0.538417	+	0.391183i	−0.823497	−	0.567321i	$-0.807980\pi$
$163$	−1120.47	+	814.069i	−0.538417	+	0.391183i	0.285080	+	0.958504i	$0.407980\pi$
$164$	−2124.08			−1.01136
$165$		0			0
$166$	2931.44			1.37062
$167$	627.204	−	455.690i	0.290626	−	0.211152i	−0.432913	−	0.901436i	$-0.642514\pi$
$167$	627.204	−	455.690i	0.290626	−	0.211152i	0.723539	+	0.690284i	$0.242514\pi$
$168$	819.003	+	2520.63i	0.376116	+	1.15756i
$169$	491.234	−	1511.86i	0.223593	−	0.688149i
$170$	2120.03	+	1540.30i	0.956466	+	0.694913i
$171$	166.714	+	121.125i	0.0745550	+	0.0541674i
$172$	205.642	−	632.901i	0.0911631	−	0.280571i
$173$	138.012	+	424.757i	0.0606523	+	0.186669i	0.976792	−	0.214191i	$-0.0687115\pi$
$173$	138.012	+	424.757i	0.0606523	+	0.186669i	−0.916140	+	0.400860i	$0.868712\pi$
$174$	3859.46	−	2804.06i	1.68152	−	1.22170i
$175$	1080.45			0.466711
$176$		0			0
$177$	5952.56			2.52781
$178$	−262.493	+	190.712i	−0.110532	+	0.0803062i
$179$	−867.487	−	2669.85i	−0.362229	−	1.11483i	−0.951698	−	0.307035i	$-0.900663\pi$
$179$	−867.487	−	2669.85i	−0.362229	−	1.11483i	0.589469	−	0.807791i	$-0.299337\pi$
$180$	−895.806	+	2757.01i	−0.370941	+	1.14164i
$181$	1080.36	+	784.930i	0.443662	+	0.322339i	0.787088	−	0.616841i	$-0.211588\pi$
$181$	1080.36	+	784.930i	0.443662	+	0.322339i	−0.343427	+	0.939180i	$0.611588\pi$
$182$	−4500.05	−	3269.48i	−1.83278	−	1.33159i
$183$	389.106	−	1197.55i	0.157178	−	0.483744i
$184$	272.653	+	839.141i	0.109241	+	0.336208i
$185$	2305.34	−	1674.93i	0.916173	−	0.665639i
$186$	8490.49			3.34706
$187$		0			0
$188$	−3059.77			−1.18700
$189$	−209.432	+	152.161i	−0.0806027	+	0.0585613i
$190$	83.7983	+	257.905i	0.0319967	+	0.0984756i
$191$	−616.479	+	1897.33i	−0.233544	+	0.718774i	0.763767	+	0.645492i	$0.223348\pi$
$191$	−616.479	+	1897.33i	−0.233544	+	0.718774i	−0.997311	+	0.0732826i	$0.976652\pi$
$192$	−5016.55	−	3644.73i	−1.88561	−	1.36998i
$193$	−1692.19	−	1229.45i	−0.631121	−	0.458537i	0.225667	−	0.974204i	$-0.427544\pi$
$193$	−1692.19	−	1229.45i	−0.631121	−	0.458537i	−0.856789	+	0.515668i	$0.827544\pi$
$194$	−1351.34	+	4159.00i	−0.500107	+	1.53917i
$195$	−1201.35	−	3697.37i	−0.441182	−	1.35782i
$196$	−646.657	+	469.824i	−0.235662	+	0.171219i
$197$	−3777.20			−1.36606			−0.683032	−	0.730389i	$-0.739339\pi$
$197$	−3777.20			−1.36606			−0.683032	+	0.730389i	$0.739339\pi$
$198$		0			0
$199$	−1251.15			−0.445688			−0.222844	−	0.974854i	$-0.571534\pi$
$199$	−1251.15			−0.445688			−0.222844	+	0.974854i	$0.571534\pi$
$200$	756.995	−	549.989i	0.267638	−	0.194451i
$201$	844.434	+	2598.90i	0.296327	+	0.912002i
$202$	−1413.19	+	4349.34i	−0.492234	+	1.51494i
$203$	2345.38	+	1704.02i	0.810902	+	0.589155i
$204$	4995.52	+	3629.46i	1.71449	+	1.24565i
$205$	465.756	−	1433.45i	0.158682	−	0.488373i
$206$	−1023.17	−	3148.98i	−0.346055	−	1.06505i
$207$	−1168.78	+	849.171i	−0.392445	+	0.285128i
$208$	1054.95			0.351670
$209$		0			0
$210$	−5710.71			−1.87655
$211$	−3724.95	+	2706.34i	−1.21534	+	0.882995i	−0.995705	−	0.0925872i	$-0.970486\pi$
$211$	−3724.95	+	2706.34i	−1.21534	+	0.882995i	−0.219634	+	0.975582i	$0.570486\pi$
$212$	786.775	+	2421.45i	0.254887	+	0.784460i
$213$	1803.69	−	5551.17i	0.580218	−	1.78573i
$214$	−4687.32	−	3405.54i	−1.49728	−	1.08784i
$215$	382.026	+	277.558i	0.121181	+	0.0880433i
$216$	−69.2784	+	213.217i	−0.0218231	+	0.0671647i
$217$	1594.41	+	4907.10i	0.498783	+	1.53510i
$218$	−2498.62	+	1815.35i	−0.776274	+	0.563996i
$219$	−7147.16			−2.20530
$220$		0			0
$221$	−4267.75			−1.29900
$222$	9075.40	−	6593.67i	2.74370	−	1.99341i
$223$	−1434.91	−	4416.19i	−0.430890	−	1.32614i	−0.897240	−	0.441543i	$-0.854431\pi$
$223$	−1434.91	−	4416.19i	−0.430890	−	1.32614i	0.466350	−	0.884600i	$-0.345569\pi$
$224$	1356.67	−	4175.41i	0.404672	−	1.24545i
$225$	1239.48	+	900.538i	0.367255	+	0.266826i
$226$	1946.58	+	1414.27i	0.572940	+	0.416266i
$227$	1316.40	−	4051.47i	0.384901	−	1.18460i	−0.551650	−	0.834075i	$-0.686002\pi$
$227$	1316.40	−	4051.47i	0.384901	−	1.18460i	0.936552	−	0.350529i	$-0.113998\pi$
$228$	197.457	+	607.710i	0.0573549	+	0.176520i
$229$	−4657.01	+	3383.51i	−1.34386	+	0.976370i	−0.344566	+	0.938762i	$0.611974\pi$
$229$	−4657.01	+	3383.51i	−1.34386	+	0.976370i	−0.999293	+	0.0376082i	$0.988026\pi$
$230$	−1901.15			−0.545034
$231$		0			0
$232$	2510.65			0.710483
$233$	−4167.31	+	3027.73i	−1.17172	+	0.851301i	−0.991213	−	0.132274i	$-0.957772\pi$
$233$	−4167.31	+	3027.73i	−1.17172	+	0.851301i	−0.180502	+	0.983575i	$0.557772\pi$
$234$	−2437.37	−	7501.44i	−0.680921	−	2.09566i
$235$	670.929	−	2064.91i	0.186241	−	0.573190i
$236$	7695.90	+	5591.40i	2.12271	+	1.54224i
$237$	−3536.12	−	2569.14i	−0.969179	−	0.704150i
$238$	−1937.24	+	5962.22i	−0.527617	+	1.62384i
$239$	−643.147	−	1979.40i	−0.174066	−	0.535720i	0.825524	−	0.564367i	$-0.190880\pi$
$239$	−643.147	−	1979.40i	−0.174066	−	0.535720i	−0.999590	+	0.0286478i	$0.990880\pi$
$240$	876.230	−	636.618i	0.235668	−	0.171223i
$241$	6829.14			1.82533			0.912663	−	0.408714i	$-0.134023\pi$
$241$	6829.14			1.82533			0.912663	+	0.408714i	$0.134023\pi$
$242$		0			0
$243$	5419.43			1.43069
$244$	1627.95	−	1182.77i	0.427126	−	0.310325i
$245$	−175.269	−	539.422i	−0.0457042	−	0.140663i
$246$	1833.53	−	5643.04i	0.475211	−	1.46255i
$247$	−357.293	−	259.588i	−0.0920404	−	0.0668713i
$248$	3614.99	+	2626.44i	0.925613	+	0.672497i
$249$	−1514.63	+	4661.55i	−0.385485	+	1.18640i
$250$	2082.53	+	6409.38i	0.526844	+	1.62146i
$251$	−16.2859	+	11.8324i	−0.00409545	+	0.00297552i	−0.589831	−	0.807527i	$-0.700806\pi$
$251$	−16.2859	+	11.8324i	−0.00409545	+	0.00297552i	0.585736	+	0.810502i	$0.300806\pi$
$252$	−6935.03			−1.73359
$253$		0			0
$254$	−3141.60			−0.776070
$255$	−3544.76	+	2575.42i	−0.870515	+	0.632466i
$256$	−669.380	−	2060.14i	−0.163423	−	0.502964i
$257$	46.6586	−	143.600i	0.0113248	−	0.0348543i	−0.945234	−	0.326392i	$-0.894167\pi$
$257$	46.6586	−	143.600i	0.0113248	−	0.0348543i	0.956559	+	0.291538i	$0.0941670\pi$
$258$	1503.92	+	1092.66i	0.362906	+	0.263667i
$259$	5515.08	+	4006.94i	1.32313	+	0.961309i
$260$	1919.85	−	5908.68i	0.457938	−	1.40939i
$261$	1270.33	+	3909.66i	0.301269	+	0.927211i
$262$	1611.89	−	1171.11i	0.380088	−	0.276150i
$263$	−2609.68			−0.611862			−0.305931	−	0.952054i	$-0.598968\pi$
$263$	−2609.68			−0.611862			−0.305931	+	0.952054i	$0.598968\pi$
$264$		0			0
$265$	−1806.65			−0.418799
$266$	−524.840	+	381.319i	−0.120977	+	0.0878953i
$267$	−167.643	−	515.953i	−0.0384255	−	0.118261i
$268$	−1349.47	+	4153.24i	−0.307582	+	0.946640i
$269$	975.627	+	708.834i	0.221134	+	0.160663i	0.692837	−	0.721094i	$-0.256361\pi$
$269$	975.627	+	708.834i	0.221134	+	0.160663i	−0.471703	+	0.881757i	$0.656361\pi$
$270$	−390.805	−	283.936i	−0.0880875	−	0.0639993i
$271$	1881.35	−	5790.19i	0.421711	−	1.29789i	−0.484398	−	0.874848i	$-0.660961\pi$
$271$	1881.35	−	5790.19i	0.421711	−	1.29789i	0.906109	−	0.423045i	$-0.139039\pi$
$272$	−367.413	−	1130.78i	−0.0819033	−	0.252072i
$273$	7524.21	−	5466.66i	1.66808	−	1.21193i
$274$	8791.94			1.93847
$275$		0			0
$276$	−4479.74			−0.976989
$277$	6030.04	−	4381.08i	1.30798	−	0.950301i	0.307978	−	0.951393i	$-0.400348\pi$
$277$	6030.04	−	4381.08i	1.30798	−	0.950301i	0.999999	+	0.00109196i	$0.000347582\pi$
$278$	356.872	+	1098.34i	0.0769920	+	0.236957i
$279$	−2260.89	+	6958.30i	−0.485147	+	1.49313i
$280$	−2431.44	−	1766.55i	−0.518952	−	0.377040i
$281$	5436.47	+	3949.83i	1.15414	+	0.838530i	0.989025	−	0.147745i	$-0.0472015\pi$
$281$	5436.47	+	3949.83i	1.15414	+	0.838530i	0.165112	+	0.986275i	$0.447202\pi$
$282$	2641.24	−	8128.89i	0.557742	−	1.71655i
$283$	−210.466	−	647.748i	−0.0442082	−	0.136059i	0.926516	−	0.376255i	$-0.122788\pi$
$283$	−210.466	−	647.748i	−0.0442082	−	0.136059i	−0.970724	+	0.240196i	$0.922788\pi$
$284$	7546.29	−	5482.70i	1.57673	−	1.14556i
$285$	−453.415			−0.0942386
$286$		0			0
$287$	3605.72			0.741600
$288$	5036.50	−	3659.23i	1.03048	−	0.748688i
$289$	−31.8431	−	98.0029i	−0.00648139	−	0.0199477i
$290$	−1671.69	+	5144.92i	−0.338499	+	1.04179i
$291$	−5915.40	−	4297.79i	−1.19164	−	0.865776i
$292$	−9240.36	−	6713.51i	−1.85189	−	1.34547i
$293$	−1767.77	+	5440.63i	−0.352471	+	1.08480i	0.604990	+	0.796233i	$0.293177\pi$
$293$	−1767.77	+	5440.63i	−0.352471	+	1.08480i	−0.957461	+	0.288562i	$0.906823\pi$
$294$	−689.979	−	2123.54i	−0.136872	−	0.421249i
$295$	−5460.91	+	3967.58i	−1.07778	+	0.783056i
$296$	5903.71			1.15928
$297$		0			0
$298$	441.179			0.0857612
$299$	2504.88	−	1819.90i	0.484485	−	0.351999i
$300$	1468.06	+	4518.21i	0.282527	+	0.869530i
$301$	−349.087	+	1074.38i	−0.0668474	+	0.205735i
$302$	−5372.35	−	3903.24i	−1.02366	−	0.743729i
$303$	−6186.11	−	4494.47i	−1.17288	−	0.852148i
$304$	38.0209	−	117.016i	0.00717318	−	0.0220768i
$305$	441.237	+	1357.99i	0.0828365	+	0.254945i
$306$	−7191.80	+	5225.15i	−1.34356	+	0.976151i
$307$	185.674			0.0345178			0.0172589	−	0.999851i	$-0.494506\pi$
$307$	185.674			0.0345178			0.0172589	+	0.999851i	$0.494506\pi$
$308$		0			0
$309$	5536.14			1.01922
$310$	−7789.22	+	5659.20i	−1.42709	+	1.03684i
$311$	784.413	+	2414.18i	0.143022	+	0.440178i	0.996751	−	0.0805398i	$-0.0256644\pi$
$311$	784.413	+	2414.18i	0.143022	+	0.440178i	−0.853729	+	0.520718i	$0.825664\pi$
$312$	2488.95	−	7660.21i	0.451632	−	1.38998i
$313$	7186.64	+	5221.40i	1.29781	+	0.942911i	0.999932	−	0.0116947i	$-0.00372262\pi$
$313$	7186.64	+	5221.40i	1.29781	+	0.942911i	0.297874	+	0.954605i	$0.403723\pi$
$314$	−7627.60	−	5541.77i	−1.37086	−	0.995988i
$315$	1520.67	−	4680.16i	0.272001	−	0.837133i
$316$	−2158.48	−	6643.13i	−0.384254	−	1.18261i
$317$	2326.18	−	1690.07i	0.412150	−	0.299444i	−0.362322	−	0.932053i	$-0.618016\pi$
$317$	2326.18	−	1690.07i	0.412150	−	0.299444i	0.774472	+	0.632609i	$0.218016\pi$
$318$	−7112.22			−1.25419
$319$		0			0
$320$	7031.54			1.22836
$321$	7837.32	−	5694.15i	1.36273	−	0.990082i
$322$	−1405.45	−	4325.52i	−0.243238	−	0.748608i
$323$	−153.812	+	473.385i	−0.0264964	+	0.0815475i
$324$	6560.35	+	4766.37i	1.12489	+	0.817279i
$325$	−2656.40	−	1929.99i	−0.453387	−	0.329405i
$326$	1910.55	−	5880.08i	0.324588	−	0.998979i
$327$	−1595.76	−	4911.25i	−0.269865	−	0.830559i
$328$	2526.28	−	1835.45i	0.425275	−	0.308981i
$329$	5194.10			0.870396
$330$		0			0
$331$	−8295.55			−1.37754			−0.688769	−	0.724981i	$-0.741848\pi$
$331$	−8295.55			−1.37754			−0.688769	+	0.724981i	$0.741848\pi$
$332$	−6336.94	+	4604.05i	−1.04754	+	0.761085i
$333$	2987.13	+	9193.46i	0.491574	+	1.51291i
$334$	−1069.47	+	3291.48i	−0.175205	+	0.539227i
$335$	−2506.94	−	1821.40i	−0.408862	−	0.297056i
$336$	2096.21	+	1522.98i	0.340350	+	0.247279i
$337$	−3138.17	+	9658.30i	−0.507261	+	1.56119i	0.289674	+	0.957125i	$0.406453\pi$
$337$	−3138.17	+	9658.30i	−0.507261	+	1.56119i	−0.796935	+	0.604065i	$0.793547\pi$
$338$	2192.92	+	6749.11i	0.352897	+	1.08610i
$339$	−3254.74	+	2364.70i	−0.521454	+	0.378859i
$340$	−7002.07			−1.11688
$341$		0			0
$342$	−919.915			−0.145448
$343$	−4521.14	+	3284.80i	−0.711716	+	0.517092i
$344$	302.319	+	930.441i	0.0473835	+	0.145831i
$345$	982.294	−	3023.19i	0.153290	−	0.471777i
$346$	−1612.97	−	1171.89i	−0.250618	−	0.182084i
$347$	9632.18	+	6998.19i	1.49015	+	1.08266i	0.974104	+	0.226099i	$0.0725972\pi$
$347$	9632.18	+	6998.19i	1.49015	+	1.08266i	0.516047	+	0.856560i	$0.327403\pi$
$348$	−3939.06	+	12123.2i	−0.606769	+	1.86744i
$349$	1403.08	+	4318.22i	0.215200	+	0.662319i	0.999139	+	0.0414806i	$0.0132075\pi$
$349$	1403.08	+	4318.22i	0.215200	+	0.662319i	−0.783939	+	0.620838i	$0.786793\pi$
$350$	−3902.08	+	2835.03i	−0.595929	+	0.432968i
$351$	786.712			0.119634
$352$		0			0
$353$	−722.250			−0.108899			−0.0544497	−	0.998517i	$-0.517340\pi$
$353$	−722.250			−0.108899			−0.0544497	+	0.998517i	$0.517340\pi$
$354$	−21497.9	+	15619.1i	−3.22768	+	2.34505i
$355$	2045.33	+	6294.89i	0.305789	+	0.941121i
$356$	267.907	−	824.532i	0.0398849	−	0.122753i
$357$	−8480.14	−	6161.18i	−1.25719	−	0.913402i
$358$	10138.5	+	7366.02i	1.49674	+	1.08745i
$359$	−3770.01	+	11602.9i	−0.554244	+	1.70579i	0.143688	+	0.989623i	$0.454104\pi$
$359$	−3770.01	+	11602.9i	−0.554244	+	1.70579i	−0.697932	+	0.716164i	$0.745896\pi$
$360$	−1316.94	−	4053.13i	−0.192803	−	0.593386i
$361$	5507.38	−	4001.34i	0.802942	−	0.583371i
$362$	−5961.37			−0.865532
$363$		0			0
$364$	14862.8			2.14017
$365$	6556.84	−	4763.82i	0.940276	−	0.683151i
$366$	1737.01	+	5345.97i	0.248074	+	0.763492i
$367$	−44.3792	+	136.585i	−0.00631219	+	0.0194269i	−0.954163	−	0.299287i	$-0.903251\pi$
$367$	−44.3792	+	136.585i	−0.00631219	+	0.0194269i	0.947851	+	0.318714i	$0.103251\pi$
$368$	697.847	+	507.015i	0.0988526	+	0.0718207i
$369$	4136.46	+	3005.31i	0.583565	+	0.423985i
$370$	−3930.92	+	12098.1i	−0.552321	+	1.69987i
$371$	−1335.59	−	4110.52i	−0.186901	−	0.575223i
$372$	−18354.0	+	13335.0i	−2.55810	+	1.85857i
$373$	−3676.93			−0.510414			−0.255207	−	0.966886i	$-0.582144\pi$
$373$	−3676.93			−0.510414			−0.255207	+	0.966886i	$0.582144\pi$
$374$		0			0
$375$	−11268.2			−1.55170
$376$	3639.14	−	2643.99i	0.499134	−	0.362642i
$377$	−2722.50	−	8379.00i	−0.371926	−	1.14467i
$378$	357.109	−	1099.07i	0.0485919	−	0.149550i
$379$	−1885.87	−	1370.17i	−0.255596	−	0.185701i	0.452607	−	0.891710i	$-0.350494\pi$
$379$	−1885.87	−	1370.17i	−0.255596	−	0.185701i	−0.708203	+	0.706009i	$0.750494\pi$
$380$	−586.207	−	425.905i	−0.0791363	−	0.0574959i
$381$	1623.22	−	4995.76i	0.218268	−	0.671760i
$382$	−2752.03	−	8469.87i	−0.368602	−	1.13444i
$383$	2998.37	−	2178.44i	0.400025	−	0.290635i	−0.369526	−	0.929220i	$-0.620480\pi$
$383$	2998.37	−	2178.44i	0.400025	−	0.290635i	0.769551	+	0.638585i	$0.220480\pi$
$384$	14734.2			1.95807
$385$		0			0
$386$	9337.39			1.23124
$387$	−1295.95	+	941.562i	−0.170224	+	0.123675i
$388$	−3610.82	−	11113.0i	−0.472453	−	1.45406i
$389$	2017.01	−	6207.72i	0.262896	−	0.809110i	−0.729275	−	0.684221i	$-0.760142\pi$
$389$	2017.01	−	6207.72i	0.262896	−	0.809110i	0.992171	−	0.124889i	$-0.0398576\pi$
$390$	14040.4	+	10200.9i	1.82298	+	1.32447i
$391$	−2823.12	−	2051.11i	−0.365143	−	0.265292i
$392$	363.122	−	1117.57i	0.0467868	−	0.143995i
$393$	1029.45	+	3168.32i	0.132134	+	0.406668i
$394$	13641.5	−	9911.13i	1.74429	−	1.26730i
$395$	4956.47			0.631359
$396$		0			0
$397$	−11290.7			−1.42736			−0.713682	−	0.700470i	$-0.752974\pi$
$397$	−11290.7			−1.42736			−0.713682	+	0.700470i	$0.752974\pi$
$398$	4518.58	−	3282.94i	0.569086	−	0.413465i
$399$	−335.193	−	1031.62i	−0.0420568	−	0.129437i
$400$	282.678	−	869.993i	0.0353347	−	0.108749i
$401$	−11173.1	−	8117.70i	−1.39141	−	1.01092i	−0.995709	−	0.0925412i	$-0.970501\pi$
$401$	−11173.1	−	8117.70i	−1.39141	−	1.01092i	−0.395703	−	0.918379i	$-0.629499\pi$
$402$	−9869.04	−	7170.28i	−1.22444	−	0.889605i
$403$	4845.43	−	14912.7i	0.598928	−	1.84331i
$404$	−3776.07	−	11621.5i	−0.465016	−	1.43117i
$405$	−4655.14	+	3382.16i	−0.571150	+	0.414965i
$406$	−12941.6			−1.58198
$407$		0			0
$408$	−9077.70			−1.10150
$409$	−7515.28	+	5460.17i	−0.908573	+	0.660117i	−0.940654	−	0.339368i	$-0.889787\pi$
$409$	−7515.28	+	5460.17i	−0.908573	+	0.660117i	0.0320802	+	0.999485i	$0.489787\pi$
$410$	2079.18	+	6399.06i	0.250447	+	0.770798i
$411$	−4542.66	+	13980.9i	−0.545190	+	1.67792i
$412$	7157.52	+	5200.24i	0.855887	+	0.621839i
$413$	−13064.2	−	9491.67i	−1.55653	−	1.13088i
$414$	1992.93	−	6133.62i	0.236588	−	0.728142i
$415$	−1717.55	−	5286.08i	−0.203160	−	0.625261i
$416$	−10794.0	+	7842.28i	−1.27216	+	0.924278i
$417$	−1930.96			−0.226762
$418$		0			0
$419$	3072.83			0.358276			0.179138	−	0.983824i	$-0.442669\pi$
$419$	3072.83			0.358276			0.179138	+	0.983824i	$0.442669\pi$
$420$	12344.9	−	8969.11i	1.43422	−	1.04202i
$421$	1846.01	+	5681.45i	0.213704	+	0.657712i	0.999243	+	0.0389005i	$0.0123855\pi$
$421$	1846.01	+	5681.45i	0.213704	+	0.657712i	−0.785539	+	0.618812i	$0.787614\pi$
$422$	6351.55	−	19548.1i	0.732674	−	2.25494i
$423$	5958.63	+	4329.20i	0.684914	+	0.497619i
$424$	−3028.16	−	2200.09i	−0.346841	−	0.251995i
$425$	−1143.56	+	3519.53i	−0.130520	+	0.401699i
$426$	8051.84	+	24781.0i	0.915758	+	2.81841i
$427$	−2763.52	+	2007.82i	−0.313200	+	0.227553i
$428$	15481.3			1.74840
$429$		0			0
$430$	−2107.99			−0.236411
$431$	188.817	−	137.184i	0.0211021	−	0.0153316i	−0.577184	−	0.816614i	$-0.695849\pi$
$431$	188.817	−	137.184i	0.0211021	−	0.0153316i	0.598286	+	0.801282i	$0.295849\pi$
$432$	67.7285	+	208.447i	0.00754303	+	0.0232151i
$433$	−1721.63	+	5298.64i	−0.191077	+	0.588075i	0.808923	+	0.587915i	$0.200051\pi$
$433$	−1721.63	+	5298.64i	−0.191077	+	0.588075i	−1.00000		0.000160200i	$0.999949\pi$
$434$	−18634.2	−	13538.5i	−2.06099	−	1.49740i
$435$	−7317.68	−	5316.61i	−0.806565	−	0.586004i
$436$	2550.15	−	7848.55i	0.280115	−	0.862104i
$437$	−111.589	−	343.435i	−0.0122151	−	0.0375943i
$438$	25812.2	−	18753.7i	2.81588	−	2.04586i
$439$	−3533.06			−0.384109			−0.192054	−	0.981384i	$-0.561515\pi$
$439$	−3533.06			−0.384109			−0.192054	+	0.981384i	$0.561515\pi$
$440$		0			0
$441$	1924.05			0.207759
$442$	15413.1	−	11198.3i	1.65866	−	1.20509i
$443$	−4605.16	−	14173.2i	−0.493900	−	1.52007i	−0.818663	−	0.574274i	$-0.805284\pi$
$443$	−4605.16	−	14173.2i	−0.493900	−	1.52007i	0.324763	−	0.945795i	$-0.394716\pi$
$444$	−9262.57	+	28507.3i	−0.990050	+	3.04706i
$445$	497.697	+	361.598i	0.0530182	+	0.0385200i
$446$	16770.0	+	12184.1i	1.78045	+	1.29358i
$447$	−227.951	+	701.560i	−0.0241201	+	0.0742341i
$448$	5198.16	+	15998.3i	0.548192	+	1.68716i
$449$	5816.95	−	4226.26i	0.611400	−	0.444208i	−0.238507	−	0.971141i	$-0.576658\pi$
$449$	5816.95	−	4226.26i	0.611400	−	0.444208i	0.849907	+	0.526932i	$0.176658\pi$
$450$	−6839.39			−0.716471
$451$		0			0
$452$	−6429.18			−0.669033
$453$	8982.72	−	6526.33i	0.931666	−	0.676895i
$454$	5876.55	+	18086.2i	0.607489	+	1.86966i
$455$	−3259.04	+	10030.3i	−0.335793	+	1.03347i
$456$	−759.978	−	552.156i	−0.0780466	−	0.0567041i
$457$	3189.31	+	2317.17i	0.326454	+	0.237183i	0.738925	−	0.673788i	$-0.235334\pi$
$457$	3189.31	+	2317.17i	0.326454	+	0.237183i	−0.412470	+	0.910971i	$0.635334\pi$
$458$	7940.82	−	24439.3i	0.810154	−	2.49340i
$459$	−273.994	−	843.265i	−0.0278626	−	0.0857522i
$460$	4109.74	−	2985.90i	0.416560	−	0.302648i
$461$	8254.37			0.833936			0.416968	−	0.908921i	$-0.363093\pi$
$461$	8254.37			0.833936			0.416968	+	0.908921i	$0.363093\pi$
$462$		0			0
$463$	7083.97			0.711058			0.355529	−	0.934665i	$-0.384301\pi$
$463$	7083.97			0.711058			0.355529	+	0.934665i	$0.384301\pi$
$464$	1985.71	−	1442.71i	0.198673	−	0.144345i
$465$	−4974.64	−	15310.4i	−0.496115	−	1.52689i
$466$	7105.83	−	21869.5i	0.706376	−	2.17400i
$467$	14464.4	+	10509.0i	1.43326	+	1.04132i	0.989398	+	0.145229i	$0.0463919\pi$
$467$	14464.4	+	10509.0i	1.43326	+	1.04132i	0.443862	+	0.896095i	$0.353608\pi$
$468$	17050.5	+	12387.9i	1.68410	+	1.22357i
$469$	2290.79	−	7050.33i	0.225541	−	0.694145i
$470$	2995.09	+	9217.95i	0.293943	+	0.904665i
$471$	12753.6	−	9266.00i	1.24767	−	0.906486i
$472$	−13984.7			−1.36377
$473$		0			0
$474$	19512.1			1.89076
$475$	−309.815	+	225.094i	−0.0299270	+	0.0217432i
$476$	−5176.37	−	15931.2i	−0.498442	−	1.53405i
$477$	1893.88	−	5828.75i	0.181792	−	0.559497i
$478$	7516.57	+	5461.11i	0.719247	+	0.522563i
$479$	3485.40	+	2532.29i	0.332468	+	0.241552i	0.741477	−	0.670978i	$-0.234126\pi$
$479$	3485.40	+	2532.29i	0.332468	+	0.241552i	−0.409009	+	0.912530i	$0.634126\pi$
$480$	−4232.88	+	13027.5i	−0.402508	+	1.23879i
$481$	−6401.88	−	19703.0i	−0.606862	−	1.86773i
$482$	−24663.7	+	17919.2i	−2.33070	+	1.69336i
$483$	7604.58			0.716399
$484$		0			0
$485$	8291.43			0.776277
$486$	−19572.5	+	14220.2i	−1.82680	+	1.32725i
$487$	4097.01	+	12609.3i	0.381218	+	1.17327i	0.939187	+	0.343406i	$0.111581\pi$
$487$	4097.01	+	12609.3i	0.381218	+	1.17327i	−0.557969	+	0.829862i	$0.688419\pi$
$488$	−914.152	+	2813.47i	−0.0847986	+	0.260983i
$489$	8363.30	+	6076.29i	0.773418	+	0.561921i
$490$	2048.40	+	1488.25i	0.188851	+	0.137209i
$491$	−283.909	+	873.783i	−0.0260950	+	0.0803121i	−0.963256	−	0.268585i	$-0.913444\pi$
$491$	−283.909	+	873.783i	−0.0260950	+	0.0803121i	0.937161	+	0.348897i	$0.113444\pi$
$492$	4899.26	+	15078.4i	0.448934	+	1.38168i
$493$	−8033.14	+	5836.42i	−0.733863	+	0.533183i
$494$	1971.52			0.179560
$495$		0			0
$496$	4368.41			0.395458
$497$	−12810.2	+	9307.16i	−1.15617	+	0.840006i
$498$	−6761.46	−	20809.6i	−0.608410	−	1.87249i
$499$	3776.49	−	11622.8i	0.338795	−	1.04270i	−0.626027	−	0.779801i	$-0.715320\pi$
$499$	3776.49	−	11622.8i	0.338795	−	1.04270i	0.964822	−	0.262903i	$-0.0846800\pi$
$500$	−14568.3	−	10584.5i	−1.30303	−	0.946705i
$501$	−4681.51	−	3401.32i	−0.417474	−	0.303313i
$502$	27.7697	−	85.4664i	0.00246897	−	0.00759871i
$503$	1696.14	+	5220.18i	0.150352	+	0.462736i	0.997660	−	0.0683654i	$-0.0217784\pi$
$503$	1696.14	+	5220.18i	0.150352	+	0.462736i	−0.847308	+	0.531101i	$0.821778\pi$
$504$	8248.19	−	5992.66i	0.728976	−	0.529632i
$505$	8670.89			0.764058
$506$		0			0
$507$	−11865.4			−1.03937
$508$	6791.26	−	4934.14i	0.593136	−	0.430939i
$509$	−28.6897	−	88.2977i	−0.00249832	−	0.00768905i	0.949800	−	0.312859i	$-0.101287\pi$
$509$	−28.6897	−	88.2977i	−0.00249832	−	0.00768905i	−0.952298	+	0.305170i	$0.901287\pi$
$510$	6044.29	−	18602.4i	0.524795	−	1.61515i
$511$	15686.0	+	11396.5i	1.35794	+	0.986599i
$512$	−4952.85	−	3598.46i	−0.427514	−	0.310607i
$513$	28.3536	−	87.2633i	0.00244023	−	0.00751027i
$514$	208.289	+	641.047i	0.0178740	+	0.0550104i
$515$	−5078.88	+	3690.02i	−0.434568	+	0.315732i
$516$	−4967.15			−0.423772
$517$		0			0
$518$	−30431.8			−2.58127
$519$	2696.93	−	1959.43i	0.228096	−	0.165722i
$520$	2822.41	+	8686.48i	0.238021	+	0.732552i
$521$	−1359.33	+	4183.60i	−0.114306	+	0.351798i	−0.991802	−	0.127787i	$-0.959213\pi$
$521$	−1359.33	+	4183.60i	−0.114306	+	0.351798i	0.877496	+	0.479585i	$0.159213\pi$
$522$	−14846.5	−	10786.6i	−1.24486	−	0.904441i
$523$	−4667.80	−	3391.36i	−0.390265	−	0.283544i	0.375299	−	0.926904i	$-0.377540\pi$
$523$	−4667.80	−	3391.36i	−0.390265	−	0.283544i	−0.765564	+	0.643359i	$0.777540\pi$
$524$	−1645.14	+	5063.21i	−0.137153	+	0.422113i
$525$	−2492.10	−	7669.88i	−0.207170	−	0.637602i
$526$	9424.95	−	6847.62i	0.781268	−	0.567625i
$527$	−17672.2			−1.46075
$528$		0			0
$529$	−9635.37			−0.791926
$530$	6524.78	−	4740.53i	0.534752	−	0.388520i
$531$	−7075.95	−	21777.5i	−0.578286	−	1.77978i
$532$	535.664	−	1648.60i	0.0436541	−	0.134354i
$533$	−8865.05	−	6440.84i	−0.720428	−	0.523422i
$534$	1959.28	+	1423.50i	0.158776	+	0.115357i
$535$	−3394.66	+	10447.7i	−0.274325	+	0.844285i
$536$	−1983.88	−	6105.77i	−0.159871	−	0.492032i
$537$	−16951.8	+	12316.2i	−1.36224	+	0.989727i
$538$	−5383.44			−0.431407
$539$		0			0
$540$	1290.75			0.102861
$541$	9332.30	−	6780.31i	0.741639	−	0.538832i	−0.151585	−	0.988444i	$-0.548438\pi$
$541$	9332.30	−	6780.31i	0.741639	−	0.538832i	0.893224	+	0.449612i	$0.148438\pi$
$542$	8398.52	+	25848.0i	0.665585	+	2.04846i
$543$	3080.15	−	9479.73i	0.243429	−	0.749197i
$544$	12165.3	+	8838.62i	0.958793	+	0.696604i
$545$	4737.47	+	3441.97i	0.372350	+	0.270528i
$546$	−12829.8	+	39486.1i	−1.00561	+	3.09496i
$547$	1004.60	+	3091.83i	0.0785254	+	0.241676i	0.982611	−	0.185674i	$-0.0594470\pi$
$547$	1004.60	+	3091.83i	0.0785254	+	0.241676i	−0.904086	+	0.427351i	$0.859447\pi$
$548$	−19005.7	+	13808.4i	−1.48154	+	1.07640i
$549$	−4843.78			−0.376552
$550$		0			0
$551$	−1027.53			−0.0794452
$552$	5327.99	−	3871.01i	0.410823	−	0.298481i
$553$	3664.13	+	11277.0i	0.281763	+	0.867177i
$554$	−10282.0	+	31644.8i	−0.788523	+	2.42682i
$555$	−17207.3	−	12501.8i	−1.31605	−	0.956168i
$556$	−2496.49	−	1813.80i	−0.190422	−	0.138350i
$557$	6235.51	−	19190.9i	0.474340	−	1.45987i	−0.372507	−	0.928029i	$-0.621502\pi$
$557$	6235.51	−	19190.9i	0.474340	−	1.45987i	0.846846	−	0.531838i	$-0.178498\pi$
$558$	−10092.8	−	31062.6i	−0.765706	−	2.35660i
$559$	2777.41	−	2017.91i	0.210147	−	0.152681i
$560$	−2938.19			−0.221717
$561$		0			0
$562$	−29998.1			−2.25159
$563$	−10464.2	+	7602.67i	−0.783326	+	0.569119i	−0.905975	−	0.423331i	$-0.860861\pi$
$563$	−10464.2	+	7602.67i	−0.783326	+	0.569119i	0.122650	+	0.992450i	$0.460861\pi$
$564$	7057.46	+	21720.6i	0.526902	+	1.62164i
$565$	1409.76	−	4338.78i	0.104971	−	0.323069i
$566$	2459.75	+	1787.12i	0.182670	+	0.132717i
$567$	−11136.5	−	8091.15i	−0.824849	−	0.599288i
$568$	−4237.52	+	13041.7i	−0.313032	+	0.963414i
$569$	−4423.73	−	13614.8i	−0.325927	−	1.00310i	−0.971020	−	0.238997i	$-0.923182\pi$
$569$	−4423.73	−	13614.8i	−0.325927	−	1.00310i	0.645093	−	0.764104i	$-0.276818\pi$
$570$	1637.52	−	1189.73i	0.120330	−	0.0874252i
$571$	−2503.96			−0.183516			−0.0917580	−	0.995781i	$-0.529249\pi$
$571$	−2503.96			−0.183516			−0.0917580	+	0.995781i	$0.529249\pi$
$572$		0			0
$573$	14890.7			1.08563
$574$	−13022.2	+	9461.18i	−0.946927	+	0.687983i
$575$	−829.641	−	2553.37i	−0.0601712	−	0.185188i
$576$	−7371.02	+	22685.7i	−0.533205	+	1.64104i
$577$	−4303.76	−	3126.86i	−0.310516	−	0.225603i	0.421602	−	0.906781i	$-0.361468\pi$
$577$	−4303.76	−	3126.86i	−0.310516	−	0.225603i	−0.732118	+	0.681178i	$0.761468\pi$
$578$	372.156	+	270.387i	0.0267814	+	0.0194578i
$579$	−4824.49	+	14848.2i	−0.346285	+	1.06575i
$580$	−4466.79	−	13747.4i	−0.319782	−	0.984187i
$581$	10757.3	−	7815.61i	0.768135	−	0.558083i
$582$	32640.8			2.32475
$583$		0			0
$584$	16791.3			1.18978
$585$	−12098.8	+	8790.30i	−0.855084	+	0.621255i
$586$	−7891.50	−	24287.5i	−0.556305	−	1.71213i
$587$	2232.54	−	6871.04i	0.156979	−	0.483132i	−0.841377	−	0.540449i	$-0.818255\pi$
$587$	2232.54	−	6871.04i	0.156979	−	0.483132i	0.998356	+	0.0573170i	$0.0182546\pi$
$588$	4826.72	+	3506.82i	0.338521	+	0.245950i
$589$	−1479.51	−	1074.92i	−0.103501	−	0.0751977i
$590$	9311.59	−	28658.1i	0.649749	−	1.99972i
$591$	8712.25	+	26813.5i	0.606386	+	1.86626i
$592$	4669.35	−	3392.48i	0.324171	−	0.235524i
$593$	26210.5			1.81507			0.907535	−	0.419976i	$-0.137962\pi$
$593$	26210.5			1.81507			0.907535	+	0.419976i	$0.137962\pi$
$594$		0			0
$595$	11886.4			0.818980
$596$	−953.704	+	692.907i	−0.0655457	+	0.0476218i
$597$	2885.83	+	8881.67i	0.197838	+	0.608882i
$598$	−4271.16	+	13145.3i	−0.292075	+	0.898913i
$599$	3292.70	+	2392.29i	0.224601	+	0.163182i	0.694395	−	0.719594i	$-0.255672\pi$
$599$	3292.70	+	2392.29i	0.224601	+	0.163182i	−0.469794	+	0.882776i	$0.655672\pi$
$600$	−5650.29	−	4105.18i	−0.384454	−	0.279322i
$601$	−514.070	+	1582.14i	−0.0348907	+	0.107383i	−0.966985	−	0.254833i	$-0.917980\pi$
$601$	−514.070	+	1582.14i	−0.0348907	+	0.107383i	0.932094	+	0.362215i	$0.117980\pi$
$602$	−1558.36	−	4796.15i	−0.105505	−	0.324711i
$603$	8504.31	−	6178.74i	0.574332	−	0.417277i
$604$	17743.8			1.19534
$605$		0			0
$606$	34134.6			2.28815
$607$	8958.87	−	6509.00i	0.599060	−	0.435243i	−0.246485	−	0.969147i	$-0.579276\pi$
$607$	8958.87	−	6509.00i	0.599060	−	0.435243i	0.845545	+	0.533904i	$0.179276\pi$
$608$	480.856	+	1479.92i	0.0320745	+	0.0987152i
$609$	6686.74	−	20579.7i	0.444927	−	1.36934i
$610$	−5156.81	−	3746.64i	−0.342284	−	0.248684i
$611$	−12770.3	−	9278.13i	−0.845547	−	0.614326i
$612$	7340.13	−	22590.6i	0.484815	−	1.49211i
$613$	4869.77	+	14987.6i	0.320862	+	0.987511i	0.973274	+	0.229647i	$0.0737572\pi$
$613$	4869.77	+	14987.6i	0.320862	+	0.987511i	−0.652412	+	0.757864i	$0.726243\pi$
$614$	−670.567	+	487.195i	−0.0440747	+	0.0320221i
$615$	−11250.0			−0.737634
$616$		0			0
$617$	19132.5			1.24837			0.624185	−	0.781277i	$-0.285431\pi$
$617$	19132.5			1.24837			0.624185	+	0.781277i	$0.285431\pi$
$618$	−19994.0	+	14526.5i	−1.30142	+	0.945534i
$619$	3169.76	+	9755.52i	0.205821	+	0.633453i	0.999679	+	0.0253491i	$0.00806974\pi$
$619$	3169.76	+	9755.52i	0.205821	+	0.633453i	−0.793857	+	0.608104i	$0.791930\pi$
$620$	7949.86	−	24467.2i	0.514958	−	1.58488i
$621$	520.410	+	378.100i	0.0336286	+	0.0244326i
$622$	−9167.57	−	6660.63i	−0.590974	−	0.429368i
$623$	−454.785	+	1399.68i	−0.0292465	+	0.0900115i
$624$	−2433.27	−	7488.84i	−0.156104	−	0.480438i
$625$	4941.43	−	3590.16i	0.316252	−	0.229770i
$626$	−39655.4			−2.53187
$627$		0			0
$628$	25192.5			1.60078
$629$	−18889.7	+	13724.2i	−1.19743	+	0.869981i
$630$	6788.45	+	20892.7i	0.429299	+	1.32125i
$631$	−836.092	+	2573.23i	−0.0527485	+	0.162343i	−0.973960	−	0.226718i	$-0.927200\pi$
$631$	−836.092	+	2573.23i	−0.0527485	+	0.162343i	0.921212	+	0.389061i	$0.127200\pi$
$632$	8307.63	+	6035.85i	0.522879	+	0.379894i
$633$	27803.4	+	20200.4i	1.74579	+	1.26839i
$634$	−3966.46	+	12207.5i	−0.248467	+	0.764703i
$635$	1840.69	+	5665.06i	0.115032	+	0.354033i
$636$	15374.6	−	11170.3i	0.958557	−	0.696432i
$637$	−4123.54			−0.256484
$638$		0			0
$639$	−22453.1			−1.39003
$640$	−13517.2	+	9820.81i	−0.834865	+	0.606565i
$641$	1658.98	+	5105.82i	0.102224	+	0.314614i	0.989069	−	0.147454i	$-0.0471077\pi$
$641$	1658.98	+	5105.82i	0.102224	+	0.314614i	−0.886845	+	0.462068i	$0.847108\pi$
$642$	−13363.7	+	41129.2i	−0.821531	+	2.52841i
$643$	−24971.4	−	18142.8i	−1.53154	−	1.11273i	−0.955378	−	0.295387i	$-0.904551\pi$
$643$	−24971.4	−	18142.8i	−1.53154	−	1.11273i	−0.576158	−	0.817339i	$-0.695449\pi$
$644$	9831.74	+	7143.18i	0.601592	+	0.437082i
$645$	1089.17	−	3352.12i	0.0664899	−	0.204635i
$646$	−686.633	−	2113.24i	−0.0418192	−	0.128706i
$647$	7097.43	−	5156.58i	0.431265	−	0.313333i	−0.350889	−	0.936417i	$-0.614121\pi$
$647$	7097.43	−	5156.58i	0.431265	−	0.313333i	0.782155	+	0.623084i	$0.214121\pi$
$648$	−11921.3			−0.722703
$649$		0			0
$650$	14657.8			0.884505
$651$	31156.9	−	22636.8i	1.87578	−	1.36284i
$652$	5105.05	+	15711.7i	0.306640	+	0.943740i
$653$	−9225.19	+	28392.2i	−0.552848	+	1.70149i	0.148713	+	0.988880i	$0.452487\pi$
$653$	−9225.19	+	28392.2i	−0.552848	+	1.70149i	−0.701561	+	0.712610i	$0.747513\pi$
$654$	18649.9	+	13550.0i	1.11509	+	0.810162i
$655$	−3056.21	−	2220.47i	−0.182314	−	0.132459i
$656$	943.364	−	2903.38i	0.0561466	−	0.172802i
$657$	8496.00	+	26148.0i	0.504506	+	1.55271i
$658$	−18758.7	+	13629.0i	−1.11138	+	0.807467i
$659$	9304.45			0.550000			0.275000	−	0.961444i	$-0.411322\pi$
$659$	9304.45			0.550000			0.275000	+	0.961444i	$0.411322\pi$
$660$		0			0
$661$	2078.54			0.122309			0.0611543	−	0.998128i	$-0.480522\pi$
$661$	2078.54			0.122309			0.0611543	+	0.998128i	$0.480522\pi$
$662$	29959.7	−	21767.0i	1.75894	−	1.27794i
$663$	9843.71	+	30295.8i	0.576619	+	1.77465i
$664$	3558.42	−	10951.7i	0.207972	−	0.640072i
$665$	995.116	+	722.994i	0.0580285	+	0.0421602i
$666$	−34911.2	−	25364.4i	−2.03120	−	1.47575i
$667$	2226.08	−	6851.16i	0.129226	−	0.397718i
$668$	−2857.64	−	8794.93i	−0.165517	−	0.509410i
$669$	−28039.9	+	20372.2i	−1.62046	+	1.17733i
$670$	13833.1			0.797643
$671$		0			0
$672$	−32769.5			−1.88112
$673$	12107.3	−	8796.46i	0.693465	−	0.503832i	−0.184333	−	0.982864i	$-0.559012\pi$
$673$	12107.3	−	8796.46i	0.693465	−	0.503832i	0.877797	+	0.479032i	$0.159012\pi$
$674$	−14009.1	−	43115.6i	−0.800610	−	2.46402i
$675$	210.803	−	648.786i	0.0120205	−	0.0369952i
$676$	−15340.5	−	11145.5i	−0.872808	−	0.634132i
$677$	18643.4	+	13545.2i	1.05838	+	0.768958i	0.973788	−	0.227457i	$-0.0730412\pi$
$677$	18643.4	+	13545.2i	1.05838	+	0.768958i	0.0845923	+	0.996416i	$0.473041\pi$
$678$	5549.76	−	17080.4i	0.314362	−	0.967506i
$679$	6129.55	+	18864.8i	0.346437	+	1.06622i
$680$	8327.93	−	6050.59i	0.469649	−	0.341220i
$681$	−31796.8			−1.78922
$682$		0			0
$683$	17860.8			1.00062			0.500312	−	0.865845i	$-0.333219\pi$
$683$	17860.8			1.00062			0.500312	+	0.865845i	$0.333219\pi$
$684$	1988.59	−	1444.80i	0.111163	−	0.0807650i
$685$	−5151.27	−	15854.0i	−0.287328	−	0.884305i
$686$	7709.15	−	23726.3i	0.429062	−	1.32052i
$687$	34760.4	+	25254.9i	1.93041	+	1.40252i
$688$	773.774	+	562.180i	0.0428777	+	0.0311525i
$689$	−4058.86	+	12491.9i	−0.224427	+	0.690716i
$690$	4385.06	+	13495.8i	0.241937	+	0.744605i
$691$	−9497.27	+	6900.17i	−0.522856	+	0.379877i	−0.817679	−	0.575675i	$-0.804739\pi$
$691$	−9497.27	+	6900.17i	−0.522856	+	0.379877i	0.294823	+	0.955552i	$0.404739\pi$
$692$	5327.32			0.292651
$693$		0			0
$694$	−53149.7			−2.90711
$695$	1771.48	−	1287.05i	0.0966847	−	0.0702456i
$696$	−5790.89	−	17822.5i	−0.315378	−	0.970634i
$697$	−3816.35	+	11745.5i	−0.207395	+	0.638297i
$698$	−16398.0	−	11913.8i	−0.889216	−	0.646053i
$699$	31105.2	+	22599.3i	1.68313	+	1.22287i
$700$	3982.56	−	12257.1i	0.215038	−	0.661819i
$701$	−9423.54	−	29002.7i	−0.507735	−	1.56265i	−0.796123	−	0.605134i	$-0.793119\pi$
$701$	−9423.54	−	29002.7i	−0.507735	−	1.56265i	0.288388	−	0.957513i	$-0.406881\pi$
$702$	−2841.24	+	2064.28i	−0.152757	+	0.110985i
$703$	−2416.21			−0.129629
$704$		0			0
$705$	−16205.8			−0.865741
$706$	2608.43	−	1895.14i	0.139050	−	0.101026i
$707$	6410.06	+	19728.1i	0.340983	+	1.04944i
$708$	21941.3	−	67528.2i	1.16469	−	3.58456i
$709$	−490.660	−	356.485i	−0.0259903	−	0.0188831i	0.574714	−	0.818354i	$-0.305113\pi$
$709$	−490.660	−	356.485i	−0.0259903	−	0.0188831i	−0.600705	+	0.799471i	$0.705113\pi$
$710$	−23904.2	−	17367.4i	−1.26353	−	0.918009i
$711$	−5195.77	+	15990.9i	−0.274060	+	0.843469i
$712$	393.855	+	1212.16i	0.0207308	+	0.0638029i
$713$	10372.4	−	7535.99i	0.544810	−	0.395828i
$714$	46792.8			2.45263
$715$		0			0
$716$	−33485.4			−1.74778
$717$	−12567.9	+	9131.12i	−0.654613	+	0.475604i
$718$	−16829.7	−	51796.5i	−0.874762	−	2.69224i
$719$	7017.39	−	21597.3i	0.363984	−	1.12023i	−0.586631	−	0.809854i	$-0.699546\pi$
$719$	7017.39	−	21597.3i	0.363984	−	1.12023i	0.950615	−	0.310373i	$-0.100454\pi$
$720$	−3370.67	−	2448.93i	−0.174469	−	0.126759i
$721$	−12150.2	−	8827.66i	−0.627598	−	0.455977i
$722$	−9390.82	+	28902.0i	−0.484058	+	1.48978i
$723$	−15751.6	−	48478.6i	−0.810249	−	2.49369i
$724$	12886.8	−	9362.80i	0.661511	−	0.480616i
$725$	−7639.50			−0.391343
$726$		0			0
$727$	34351.1			1.75243			0.876213	−	0.481925i	$-0.160062\pi$
$727$	34351.1			1.75243			0.876213	+	0.481925i	$0.160062\pi$
$728$	−17677.1	+	12843.2i	−0.899942	+	0.653846i
$729$	−6828.05	−	21014.6i	−0.346901	−	1.06765i
$730$	−11180.3	+	34409.4i	−0.566851	+	1.74459i
$731$	−3130.28	−	2274.28i	−0.158382	−	0.115071i
$732$	−12151.2	−	8828.35i	−0.613553	−	0.445772i
$733$	−493.821	+	1519.83i	−0.0248836	+	0.0765840i	−0.962727	−	0.270474i	$-0.912819\pi$
$733$	−493.821	+	1519.83i	−0.0248836	+	0.0765840i	0.937844	+	0.347058i	$0.112819\pi$
$734$	−198.113	−	609.729i	−0.00996252	−	0.0306615i
$735$	−3424.98	+	2488.39i	−0.171881	+	0.124879i
$736$	−10909.3			−0.546360
$737$		0			0
$738$	−22824.7			−1.13847
$739$	−11473.6	+	8336.03i	−0.571126	+	0.414947i	−0.835514	−	0.549469i	$-0.814830\pi$
$739$	−11473.6	+	8336.03i	−0.571126	+	0.414947i	0.264388	+	0.964416i	$0.414830\pi$
$740$	−10503.5	−	32326.5i	−0.521780	−	1.60587i
$741$	−1018.65	+	3135.09i	−0.0505009	+	0.155426i
$742$	15609.3	+	11340.8i	0.772283	+	0.561097i
$743$	28113.3	+	20425.5i	1.38813	+	1.00853i	0.996068	+	0.0885912i	$0.0282365\pi$
$743$	28113.3	+	20425.5i	1.38813	+	1.00853i	0.392057	+	0.919941i	$0.371764\pi$
$744$	10306.5	−	31720.0i	0.507867	−	1.56305i
$745$	−258.490	−	795.551i	−0.0127119	−	0.0391232i
$746$	13279.4	−	9648.02i	0.651732	−	0.473511i
$747$	18854.8			0.923510
$748$		0			0
$749$	−26280.3			−1.28206
$750$	40695.4	−	29566.9i	1.98131	−	1.43951i
$751$	−8615.14	−	26514.7i	−0.418603	−	1.28833i	−0.908988	−	0.416822i	$-0.863144\pi$
$751$	−8615.14	−	26514.7i	−0.418603	−	1.28833i	0.490385	−	0.871506i	$-0.336856\pi$
$752$	1358.93	−	4182.36i	0.0658978	−	0.202812i
$753$	121.560	+	88.3184i	0.00588299	+	0.00427424i
$754$	31818.3	+	23117.4i	1.53681	+	1.11656i
$755$	−3890.77	+	11974.6i	−0.187549	+	0.577217i
$756$	954.206	+	2936.74i	0.0459050	+	0.141281i
$757$	6412.71	−	4659.11i	0.307892	−	0.223696i	−0.423100	−	0.906083i	$-0.639058\pi$
$757$	6412.71	−	4659.11i	0.307892	−	0.223696i	0.730991	+	0.682387i	$0.239058\pi$
$758$	10406.1			0.498638
$759$		0			0
$760$	1065.24			0.0508424
$761$	7491.48	−	5442.88i	0.356854	−	0.259270i	−0.394885	−	0.918731i	$-0.629215\pi$
$761$	7491.48	−	5442.88i	0.356854	−	0.259270i	0.751739	+	0.659461i	$0.229215\pi$
$762$	7246.22	+	22301.6i	0.344492	+	1.06024i
$763$	−4329.00	+	13323.3i	−0.205400	+	0.632157i
$764$	19251.7	+	13987.2i	0.911652	+	0.662354i
$765$	13635.9	+	9907.08i	0.644455	+	0.468224i
$766$	−5112.63	+	15735.0i	−0.241158	+	0.742207i
$767$	15164.8	+	46672.5i	0.713911	+	2.19719i
$768$	−13080.5	+	9503.57i	−0.614587	+	0.446524i
$769$	−30944.5			−1.45109			−0.725545	−	0.688175i	$-0.758412\pi$
$769$	−30944.5			−1.45109			−0.725545	+	0.688175i	$0.758412\pi$
$770$		0			0
$771$	−1127.01			−0.0526436
$772$	−20184.8	+	14665.1i	−0.941018	+	0.683690i
$773$	4645.07	+	14296.1i	0.216134	+	0.665192i	0.999071	+	0.0430912i	$0.0137206\pi$
$773$	4645.07	+	14296.1i	0.216134	+	0.665192i	−0.782937	+	0.622101i	$0.786279\pi$
$774$	2209.77	−	6800.97i	0.102621	−	0.315834i
$775$	−10999.8	−	7991.85i	−0.509840	−	0.370420i
$776$	13897.4	+	10097.1i	0.642898	+	0.467092i
$777$	15723.7	−	48392.5i	0.725976	−	2.23433i
$778$	9004.14	+	27711.9i	0.414928	+	1.27702i
$779$	−1033.93	+	751.193i	−0.0475537	+	0.0345498i
$780$	−46372.7			−2.12873
$781$		0			0
$782$	15577.8			0.712352
$783$	1480.82	−	1075.88i	0.0675865	−	0.0491045i
$784$	−354.998	−	1092.57i	−0.0161716	−	0.0497709i
$785$	−5524.07	+	17001.3i	−0.251162	+	0.772999i
$786$	−12031.3	−	8741.28i	−0.545984	−	0.396681i
$787$	5444.60	+	3955.73i	0.246606	+	0.179170i	0.704221	−	0.709981i	$-0.251296\pi$
$787$	5444.60	+	3955.73i	0.246606	+	0.179170i	−0.457615	+	0.889150i	$0.651296\pi$
$788$	−13922.8	+	42850.1i	−0.629417	+	1.93715i
$789$	6019.31	+	18525.5i	0.271601	+	0.835902i
$790$	−17900.5	+	13005.4i	−0.806164	+	0.585712i
$791$	10913.8			0.490584
$792$		0			0
$793$	10380.9			0.464865
$794$	40776.7	−	29626.0i	1.82256	−	1.32417i
$795$	4167.10	+	12825.0i	0.185902	+	0.572147i
$796$	−4611.77	+	14193.6i	−0.205352	+	0.632008i
$797$	14680.7	+	10666.1i	0.652467	+	0.474045i	0.864111	−	0.503302i	$-0.167882\pi$
$797$	14680.7	+	10666.1i	0.652467	+	0.474045i	−0.211644	+	0.977347i	$0.567882\pi$
$798$	3917.46	+	2846.20i	0.173780	+	0.126259i
$799$	−5497.51	+	16919.6i	−0.243414	+	0.749152i
$800$	3575.07	+	11002.9i	0.157997	+	0.486266i
$801$	−1688.34	+	1226.65i	−0.0744750	+	0.0541093i
$802$	61652.2			2.71448
$803$		0			0
$804$	32595.6			1.42980
$805$	−6976.48	+	5068.71i	−0.305452	+	0.221924i
$806$	21630.5	+	66571.8i	0.945287	+	2.90929i
$807$	2781.54	−	8560.71i	0.121332	−	0.373422i
$808$	14533.4	+	10559.2i	0.632778	+	0.459740i
$809$	−23426.5	−	17020.3i	−1.01808	−	0.739682i	−0.0521954	−	0.998637i	$-0.516622\pi$
$809$	−23426.5	−	17020.3i	−1.01808	−	0.739682i	−0.965889	+	0.258955i	$0.916622\pi$
$810$	7937.64	−	24429.5i	0.344321	−	1.05971i
$811$	−825.006	−	2539.11i	−0.0357212	−	0.109938i	0.931606	−	0.363470i	$-0.118408\pi$
$811$	−825.006	−	2539.11i	−0.0357212	−	0.109938i	−0.967327	+	0.253531i	$0.918408\pi$
$812$	27976.1	−	20325.8i	1.20908	−	0.878445i
$813$	−45442.7			−1.96032
$814$		0			0
$815$	−11722.6			−0.503833
$816$	−7179.72	+	5216.37i	−0.308015	+	0.223786i
$817$	−123.730	−	380.801i	−0.00529836	−	0.0163067i
$818$	12814.6	−	39439.2i	0.547739	−	1.68577i
$819$	−28944.1	−	21029.1i	−1.23490	−	0.897211i
$820$	−14544.8	−	10567.4i	−0.619424	−	0.450038i
$821$	2540.72	−	7819.53i	0.108004	−	0.332404i	−0.882419	−	0.470464i	$-0.844087\pi$
$821$	2540.72	−	7819.53i	0.108004	−	0.332404i	0.990424	+	0.138060i	$0.0440867\pi$
$822$	−20278.9	−	62412.1i	−0.860473	−	2.64826i
$823$	−13266.6	+	9638.75i	−0.561901	+	0.408245i	−0.832154	−	0.554544i	$-0.812893\pi$
$823$	−13266.6	+	9638.75i	−0.561901	+	0.408245i	0.270253	+	0.962789i	$0.412893\pi$
$824$	−13006.4			−0.549879
$825$		0			0
$826$	72087.2			3.03660
$827$	−18227.6	+	13243.1i	−0.766427	+	0.556842i	−0.900875	−	0.434079i	$-0.857074\pi$
$827$	−18227.6	+	13243.1i	−0.766427	+	0.556842i	0.134448	+	0.990921i	$0.457074\pi$
$828$	5325.17	+	16389.2i	0.223505	+	0.687879i
$829$	−4088.07	+	12581.8i	−0.171272	+	0.527121i	−0.999444	−	0.0333535i	$-0.989381\pi$
$829$	−4088.07	+	12581.8i	−0.171272	+	0.527121i	0.828172	+	0.560475i	$0.189381\pi$
$830$	20073.3	+	14584.1i	0.839464	+	0.609906i
$831$	−45008.8	−	32700.8i	−1.87887	−	1.36508i
$832$	15797.2	−	48618.8i	0.658257	−	2.02591i
$833$	1436.13	+	4419.96i	0.0597347	+	0.183845i
$834$	6973.74	−	5066.72i	0.289545	−	0.210367i
$835$	6561.93			0.271958
$836$		0			0
$837$	3257.68			0.134530
$838$	−11097.6	+	8062.91i	−0.457472	+	0.332373i
$839$	1013.35	+	3118.78i	0.0416983	+	0.128334i	0.969739	−	0.244146i	$-0.0785076\pi$
$839$	1013.35	+	3118.78i	0.0416983	+	0.128334i	−0.928040	+	0.372480i	$0.878508\pi$
$840$	−6932.12	+	21334.9i	−0.284739	+	0.876337i
$841$	3147.76	+	2286.98i	0.129065	+	0.0937711i
$842$	−21574.7	−	15674.9i	−0.883031	−	0.641560i
$843$	15499.6	−	47702.7i	0.633254	−	1.94895i
$844$	16971.5	+	52233.0i	0.692161	+	2.13025i
$845$	10885.4	−	7908.71i	0.443159	−	0.321974i
$846$	−32879.3			−1.33619
$847$		0			0
$848$	−3659.28			−0.148184
$849$	−4112.78	+	2988.11i	−0.166255	+	0.120791i
$850$	−5104.98	−	15711.5i	−0.205999	−	0.634001i
$851$	5234.55	−	16110.3i	0.210856	−	0.648947i
$852$	−56326.3	−	40923.5i	−2.26491	−	1.64556i
$853$	−27600.1	−	20052.6i	−1.10786	−	0.804911i	−0.125538	−	0.992089i	$-0.540066\pi$
$853$	−27600.1	−	20052.6i	−1.10786	−	0.804911i	−0.982326	+	0.187178i	$0.940066\pi$
$854$	4712.18	−	14502.6i	0.188814	−	0.581111i
$855$	538.985	+	1658.83i	0.0215589	+	0.0663516i
$856$	−18412.7	+	13377.6i	−0.735204	+	0.534157i
$857$	−5029.20			−0.200460			−0.100230	−	0.994964i	$-0.531958\pi$
$857$	−5029.20			−0.200460			−0.100230	+	0.994964i	$0.531958\pi$
$858$		0			0
$859$	−3540.39			−0.140625			−0.0703124	−	0.997525i	$-0.522400\pi$
$859$	−3540.39			−0.140625			−0.0703124	+	0.997525i	$0.522400\pi$
$860$	4556.89	−	3310.77i	0.180684	−	0.131275i
$861$	−8316.73	−	25596.3i	−0.329191	−	1.01315i
$862$	−321.958	+	990.886i	−0.0127215	+	0.0391528i
$863$	8449.44	+	6138.88i	0.333282	+	0.242143i	0.741822	−	0.670597i	$-0.233962\pi$
$863$	8449.44	+	6138.88i	0.333282	+	0.242143i	−0.408540	+	0.912740i	$0.633962\pi$
$864$	−2242.54	−	1629.30i	−0.0883018	−	0.0641550i
$865$	−1168.15	+	3595.18i	−0.0459169	+	0.141318i
$866$	−7685.55	−	23653.7i	−0.301577	−	0.928158i
$867$	−622.254	+	452.094i	−0.0243747	+	0.0177093i
$868$	61545.1			2.40666
$869$		0			0
$870$	40378.5			1.57352
$871$	−18226.0	+	13242.0i	−0.709030	+	0.515141i
$872$	3749.03	+	11538.3i	0.145594	+	0.448092i
$873$	−8691.74	+	26750.4i	−0.336965	+	1.03707i
$874$	1304.16	+	947.526i	0.0504734	+	0.0366711i
$875$	24730.4	+	17967.7i	0.955474	+	0.694192i
$876$	−26344.6	+	81080.2i	−1.01610	+	3.12722i
$877$	−5340.72	−	16437.0i	−0.205637	−	0.632884i	−0.999687	−	0.0250320i	$-0.992031\pi$
$877$	−5340.72	−	16437.0i	−0.205637	−	0.632884i	0.794050	−	0.607852i	$-0.207969\pi$
$878$	12759.8	−	9270.51i	0.490457	−	0.356338i
$879$	42699.3			1.63847
$880$		0			0
$881$	−6262.31			−0.239481			−0.119740	−	0.992805i	$-0.538206\pi$
$881$	−6262.31			−0.239481			−0.119740	+	0.992805i	$0.538206\pi$
$882$	−6948.79	+	5048.59i	−0.265281	+	0.192738i
$883$	9088.07	+	27970.2i	0.346362	+	1.06599i	0.960850	+	0.277067i	$0.0893626\pi$
$883$	9088.07	+	27970.2i	0.346362	+	1.06599i	−0.614488	+	0.788926i	$0.710637\pi$
$884$	−15731.0	+	48415.0i	−0.598519	+	1.84205i
$885$	40760.8	+	29614.4i	1.54820	+	1.12483i
$886$	53821.3	+	39103.5i	2.04082	+	1.48274i
$887$	−3672.59	+	11303.1i	−0.139023	+	0.427869i	−0.996194	−	0.0871630i	$-0.972220\pi$
$887$	−3672.59	+	11303.1i	−0.139023	+	0.427869i	0.857171	+	0.515032i	$0.172220\pi$
$888$	−13617.1	−	41909.1i	−0.514595	−	1.58376i
$889$	−11528.5	+	8375.94i	−0.434931	+	0.315996i
$890$	−2746.26			−0.103432
$891$		0			0
$892$	−55388.1			−2.07907
$893$	−1489.39	+	1082.11i	−0.0558125	+	0.0405502i
$894$	−1017.60	−	3131.84i	−0.0380688	−	0.117164i
$895$	7342.49	−	22597.9i	0.274226	−	0.843982i
$896$	−32337.2	−	23494.4i	−1.20570	−	0.875995i
$897$	−18696.7	−	13583.9i	−0.695946	−	0.505634i
$898$	−9918.68	+	30526.6i	−0.368587	+	1.13439i
$899$	−11273.6	−	34696.4i	−0.418236	−	1.28720i
$900$	14784.8	−	10741.8i	0.547586	−	0.397844i
$901$	14803.5			0.547365
$902$		0			0
$903$	8431.98			0.310740
$904$	7646.56	−	5555.55i	0.281328	−	0.204397i
$905$	3492.81	+	10749.8i	0.128293	+	0.394845i
$906$	−15316.7	+	47140.1i	−0.561661	+	1.72861i
$907$	−35640.6	−	25894.4i	−1.30477	−	0.947972i	−0.304781	−	0.952422i	$-0.598583\pi$
$907$	−35640.6	−	25894.4i	−1.30477	−	0.947972i	−0.999990	+	0.00445054i	$0.998583\pi$
$908$	−41109.2	−	29867.6i	−1.50248	−	1.09162i
$909$	−9089.52	+	27974.7i	−0.331661	+	1.02075i
$910$	−14548.7	−	44776.2i	−0.529982	−	1.63112i
$911$	28867.5	−	20973.5i	1.04986	−	0.762768i	0.0776742	−	0.996979i	$-0.475251\pi$
$911$	28867.5	−	20973.5i	1.04986	−	0.762768i	0.972186	+	0.234211i	$0.0752506\pi$
$912$	−918.369			−0.0333446
$913$		0			0
$914$	−17598.4			−0.636874
$915$	8622.32	−	6264.48i	0.311525	−	0.226336i
$916$	21218.1	+	65302.6i	0.765356	+	2.35552i
$917$	2792.70	−	8595.05i	0.100570	−	0.309524i
$918$	3202.21	+	2326.54i	0.115129	+	0.0836463i
$919$	−4688.30	−	3406.25i	−0.168284	−	0.122265i	0.500456	−	0.865762i	$-0.333166\pi$
$919$	−4688.30	−	3406.25i	−0.168284	−	0.122265i	−0.668739	+	0.743497i	$0.733166\pi$
$920$	−2307.77	+	7102.57i	−0.0827009	+	0.254527i
$921$	−428.263	−	1318.06i	−0.0153222	−	0.0471568i
$922$	−29810.9	+	21658.9i	−1.06483	+	0.773643i
$923$	48120.4			1.71604
$924$		0			0
$925$	−17964.1			−0.638545
$926$	−25584.0	+	18587.9i	−0.907929	+	0.659649i
$927$	−6580.94	−	20254.0i	−0.233168	−	0.717616i
$928$	−9592.57	+	29522.9i	−0.339323	+	1.04433i
$929$	28252.2	+	20526.5i	0.997768	+	0.724921i	0.961608	−	0.274425i	$-0.0884876\pi$
$929$	28252.2	+	20526.5i	0.997768	+	0.724921i	0.0361593	+	0.999346i	$0.488488\pi$
$930$	58139.5	+	42240.8i	2.04997	+	1.48939i
$931$	−148.615	+	457.389i	−0.00523163	+	0.0161013i
$932$	18987.0	+	58435.9i	0.667317	+	2.05379i
$933$	15328.4	−	11136.8i	0.537867	−	0.390784i
$934$	−79813.6			−2.79612
$935$		0			0
$936$	−30983.6			−1.08198
$937$	16008.2	−	11630.6i	0.558127	−	0.405503i	−0.272646	−	0.962114i	$-0.587899\pi$
$937$	16008.2	−	11630.6i	0.558127	−	0.405503i	0.830773	+	0.556612i	$0.187899\pi$
$938$	10226.3	+	31473.4i	0.355972	+	1.09557i
$939$	20489.4	−	63059.7i	0.712082	−	2.19156i
$940$	−20952.1	−	15222.6i	−0.727001	−	0.528197i
$941$	15027.6	+	10918.2i	0.520602	+	0.378239i	0.816831	−	0.576878i	$-0.195729\pi$
$941$	15027.6	+	10918.2i	0.520602	+	0.378239i	−0.296229	+	0.955117i	$0.595729\pi$
$942$	−21746.5	+	66928.9i	−0.752166	+	2.31493i
$943$	−2768.71	−	8521.22i	−0.0956116	−	0.294262i
$944$	−11060.8	+	8036.13i	−0.381354	+	0.277070i
$945$	−2191.12			−0.0754255
$946$		0			0
$947$	24620.0			0.844817			0.422408	−	0.906406i	$-0.361185\pi$
$947$	24620.0			0.844817			0.422408	+	0.906406i	$0.361185\pi$
$948$	−42179.5	+	30645.2i	−1.44507	+	1.04991i
$949$	−18208.2	−	56039.1i	−0.622827	−	1.91687i
$950$	528.277	−	1625.87i	0.0180417	−	0.0555265i
$951$	−17362.9	−	12614.9i	−0.592040	−	0.430142i
$952$	19922.9	+	14474.9i	0.678263	+	0.492787i
$953$	−8229.75	+	25328.6i	−0.279735	+	0.860937i	0.708192	+	0.706020i	$0.249511\pi$
$953$	−8229.75	+	25328.6i	−0.279735	+	0.860937i	−0.987927	+	0.154917i	$0.950489\pi$
$954$	8454.45	+	26020.1i	0.286921	+	0.883053i
$955$	−13660.8	+	9925.12i	−0.462881	+	0.336303i
$956$	−24825.8			−0.839878
$957$		0			0
$958$	−19232.2			−0.648607
$959$	32263.1	−	23440.5i	1.08637	−	0.789294i
$960$	−16218.5	−	49915.4i	−0.545260	−	1.67814i
$961$	10858.4	−	33418.7i	0.364486	−	1.12177i
$962$	74819.9	+	54359.8i	2.50758	+	1.82186i
$963$	−30148.5	−	21904.2i	−1.00885	−	0.732972i
$964$	25172.3	−	77472.4i	0.841023	−	2.58840i
$965$	−5470.85	−	16837.5i	−0.182500	−	0.561678i
$966$	−27464.2	+	19953.9i	−0.914748	+	0.664603i
$967$	−20484.3			−0.681210			−0.340605	−	0.940207i	$-0.610632\pi$
$967$	−20484.3			−0.681210			−0.340605	+	0.940207i	$0.610632\pi$
$968$		0			0
$969$	3715.23			0.123169
$970$	−29944.8	+	21756.2i	−0.991205	+	0.720153i
$971$	−17132.3	−	52727.8i	−0.566222	−	1.74265i	−0.664291	−	0.747474i	$-0.731267\pi$
$971$	−17132.3	−	52727.8i	−0.566222	−	1.74265i	0.0980691	−	0.995180i	$-0.468733\pi$
$972$	19976.1	−	61480.2i	0.659192	−	2.02878i
$973$	4237.91	+	3079.02i	0.139631	+	0.101448i
$974$	−47882.4	−	34788.6i	−1.57521	−	1.14446i
$975$	−7573.49	+	23308.8i	−0.248765	+	0.765620i
$976$	893.701	+	2750.53i	0.0293101	+	0.0902073i
$977$	−47418.8	+	34451.8i	−1.55278	+	1.12816i	−0.611141	+	0.791522i	$0.709289\pi$
$977$	−47418.8	+	34451.8i	−1.55278	+	1.12816i	−0.941635	+	0.336635i	$0.890711\pi$
$978$	−46148.1			−1.50885
$979$		0			0
$980$	−6765.46			−0.220525
$981$	−16070.9	+	11676.2i	−0.523044	+	0.380013i
$982$	−1267.40	−	3900.65i	−0.0411857	−	0.126757i
$983$	−9587.60	+	29507.6i	−0.311085	+	0.957422i	0.666251	+	0.745728i	$0.267898\pi$
$983$	−9587.60	+	29507.6i	−0.311085	+	0.957422i	−0.977336	+	0.211694i	$0.932102\pi$
$984$	−18856.4	−	13700.0i	−0.610894	−	0.443840i
$985$	−25864.8	−	18791.9i	−0.836670	−	0.607877i
$986$	13697.6	−	42156.9i	0.442414	−	1.36161i
$987$	−11980.4	−	36871.8i	−0.386362	−	1.18910i
$988$	−4261.86	+	3096.42i	−0.137235	+	0.0997068i
$989$	2807.08			0.0902528
$990$		0			0
$991$	11965.1			0.383537			0.191769	−	0.981440i	$-0.438578\pi$
$991$	11965.1			0.383537			0.191769	+	0.981440i	$0.438578\pi$
$992$	−44696.6	+	32473.9i	−1.43056	+	1.03936i
$993$	19134.0	+	58888.3i	0.611479	+	1.88194i
$994$	21843.1	−	67226.2i	0.697004	−	2.14516i
$995$	−8567.40	−	6224.58i	−0.272970	−	0.198324i
$996$	47299.5	+	34365.1i	1.50476	+	1.09327i
$997$	−10273.8	+	31619.4i	−0.326352	+	1.00441i	0.644475	+	0.764626i	$0.277076\pi$
$997$	−10273.8	+	31619.4i	−0.326352	+	1.00441i	−0.970827	+	0.239782i	$0.922924\pi$
$998$	16858.6	+	51885.5i	0.534720	+	1.64570i
$999$	3482.10	−	2529.90i	0.110279	−	0.0801225i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.4.c.d.3.1		8
11.2	odd	10		121.4.a.b.1.1	✓	2
11.3	even	5	inner	121.4.c.d.27.2		8
11.4	even	5	inner	121.4.c.d.81.1		8
11.5	even	5	inner	121.4.c.d.9.2		8
11.6	odd	10		121.4.c.g.9.1		8
11.7	odd	10		121.4.c.g.81.2		8
11.8	odd	10		121.4.c.g.27.1		8
11.9	even	5		121.4.a.e.1.2	yes	2
11.10	odd	2		121.4.c.g.3.2		8
33.2	even	10		1089.4.a.x.1.2		2
33.20	odd	10		1089.4.a.k.1.1		2
44.31	odd	10		1936.4.a.y.1.2		2
44.35	even	10		1936.4.a.z.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
121.4.a.b.1.1	✓	2	11.2	odd	10
121.4.a.e.1.2	yes	2	11.9	even	5
121.4.c.d.3.1		8	1.1	even	1	trivial
121.4.c.d.9.2		8	11.5	even	5	inner
121.4.c.d.27.2		8	11.3	even	5	inner
121.4.c.d.81.1		8	11.4	even	5	inner
121.4.c.g.3.2		8	11.10	odd	2
121.4.c.g.9.1		8	11.6	odd	10
121.4.c.g.27.1		8	11.8	odd	10
121.4.c.g.81.2		8	11.7	odd	10
1089.4.a.k.1.1		2	33.20	odd	10
1089.4.a.x.1.2		2	33.2	even	10
1936.4.a.y.1.2		2	44.31	odd	10
1936.4.a.z.1.2		2	44.35	even	10

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:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	121.c (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.61153 + 2.62393i) q^{2} +(-2.30653 - 7.09878i) q^{3} +(3.68602 - 11.3444i) q^{4} +(6.84760 + 4.97507i) q^{5} +(26.9569 + 19.5853i) q^{6} +(-6.25720 + 19.2577i) q^{7} +(5.41889 + 16.6776i) q^{8} +(-23.2292 + 16.8770i) q^{9} -37.7846 q^{10} -89.0333 q^{12} +(49.7836 - 36.1699i) q^{13} +(-27.9328 - 85.9682i) q^{14} +(19.5227 - 60.0848i) q^{15} +(13.8695 + 10.0768i) q^{16} +(-56.1084 - 40.7652i) q^{17} +(39.6088 - 121.903i) q^{18} +(-2.21779 - 6.82565i) q^{19} +(81.6796 - 59.3437i) q^{20} +151.138 q^{21} +50.3154 q^{23} +(105.892 - 76.9351i) q^{24} +(-16.4888 - 50.7474i) q^{25} +(-84.8877 + 261.258i) q^{26} +(10.3430 + 7.51461i) q^{27} +(195.402 + 141.968i) q^{28} +(44.2425 - 136.164i) q^{29} +(87.1515 + 268.225i) q^{30} +(206.148 - 149.775i) q^{31} -216.818 q^{32} +309.603 q^{34} +(-138.655 + 100.739i) q^{35} +(105.836 + 325.730i) q^{36} +(104.035 - 320.187i) q^{37} +(25.9197 + 18.8317i) q^{38} +(-371.590 - 269.976i) q^{39} +(-45.8660 + 141.161i) q^{40} +(-55.0272 - 169.356i) q^{41} +(-545.842 + 396.577i) q^{42} +55.7898 q^{43} -243.028 q^{45} +(-181.716 + 132.024i) q^{46} +(-79.2676 - 243.961i) q^{47} +(39.5423 - 121.699i) q^{48} +(-54.2125 - 39.3877i) q^{49} +(192.708 + 140.010i) q^{50} +(-159.967 + 492.328i) q^{51} +(-226.822 - 698.088i) q^{52} +(-172.684 + 125.462i) q^{53} -57.0718 q^{54} -355.079 q^{56} +(-43.3384 + 31.4872i) q^{57} +(197.503 + 607.852i) q^{58} +(-246.439 + 758.460i) q^{59} +(-609.665 - 442.947i) q^{60} +(136.479 + 99.1578i) q^{61} +(-351.510 + 1081.84i) q^{62} +(-179.662 - 552.942i) q^{63} +(672.090 - 488.302i) q^{64} +520.846 q^{65} -366.105 q^{67} +(-669.273 + 486.255i) q^{68} +(-116.054 - 357.178i) q^{69} +(236.426 - 727.644i) q^{70} +(632.643 + 459.642i) q^{71} +(-407.344 - 295.953i) q^{72} +(295.896 - 910.673i) q^{73} +(464.422 + 1429.35i) q^{74} +(-322.213 + 234.101i) q^{75} -85.6077 q^{76} +2050.41 q^{78} +(473.750 - 344.199i) q^{79} +(44.8399 + 138.003i) q^{80} +(-210.076 + 646.548i) q^{81} +(643.112 + 467.248i) q^{82} +(-531.257 - 385.980i) q^{83} +(557.099 - 1714.57i) q^{84} +(-181.398 - 558.287i) q^{85} +(-201.487 + 146.389i) q^{86} -1068.65 q^{87} +72.6819 q^{89} +(877.705 - 637.690i) q^{90} +(385.042 + 1185.04i) q^{91} +(185.463 - 570.797i) q^{92} +(-1538.71 - 1117.94i) q^{93} +(926.414 + 673.079i) q^{94} +(18.7716 - 57.7730i) q^{95} +(500.098 + 1539.14i) q^{96} +(792.513 - 575.794i) q^{97} +299.141 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 8 q^{3} - 10 q^{4} + 10 q^{5} + 32 q^{6} - 8 q^{7} - 42 q^{8} - 2 q^{9} - 136 q^{10} - 352 q^{12} + 130 q^{13} + 160 q^{14} - 64 q^{15} + 62 q^{16} - 14 q^{17} - 194 q^{18} - 48 q^{19} + 98 q^{20}+ \cdots - 3288 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 + 8 * q^3 - 10 * q^4 + 10 * q^5 + 32 * q^6 - 8 * q^7 - 42 * q^8 - 2 * q^9 - 136 * q^10 - 352 * q^12 + 130 * q^13 + 160 * q^14 - 64 * q^15 + 62 * q^16 - 14 * q^17 - 194 * q^18 - 48 * q^19 + 98 * q^20 + 544 * q^21 - 512 * q^23 + 144 * q^24 + 176 * q^25 + 106 * q^26 - 16 * q^27 + 296 * q^28 - 30 * q^29 - 280 * q^30 + 184 * q^31 - 1208 * q^32 + 1784 * q^34 - 128 * q^35 - 394 * q^36 - 126 * q^37 + 168 * q^38 - 496 * q^39 + 186 * q^40 + 370 * q^41 - 712 * q^42 + 1056 * q^43 - 808 * q^45 - 664 * q^46 - 256 * q^47 - 152 * q^48 - 522 * q^49 - 64 * q^50 + 488 * q^51 + 602 * q^52 + 162 * q^53 - 512 * q^54 + 1344 * q^56 - 24 * q^57 - 918 * q^58 + 1304 * q^59 - 752 * q^60 - 300 * q^61 + 1312 * q^62 + 1336 * q^63 + 262 * q^64 + 2504 * q^65 - 2624 * q^67 - 934 * q^68 + 280 * q^69 - 872 * q^70 + 1176 * q^71 + 150 * q^72 - 668 * q^73 - 2022 * q^74 - 464 * q^75 - 768 * q^76 + 7840 * q^78 + 416 * q^79 - 214 * q^80 - 26 * q^81 + 322 * q^82 - 960 * q^83 - 1832 * q^84 + 502 * q^85 + 264 * q^86 - 4032 * q^87 - 4296 * q^89 + 1186 * q^90 + 688 * q^91 - 944 * q^92 - 1864 * q^93 + 2408 * q^94 + 24 * q^95 - 1664 * q^96 + 338 * q^97 - 3288 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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