LMFDB - Embedded newform 230.4.e.a.137.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,4,Mod(137,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("230.137");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	230.e (of order $4$, degree $2$, 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:	$13.5704393013$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			137.2
Character	$\chi$	$=$	230.137
Dual form			230.4.e.a.183.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41421 - 1.41421i) q^{2} +(-7.12210 + 7.12210i) q^{3} +4.00000i q^{4} +(1.63222 + 11.0606i) q^{5} +20.1443 q^{6} +(16.1147 - 16.1147i) q^{7} +(5.65685 - 5.65685i) q^{8} -74.4485i q^{9} +O(q^{10})$	\(q+(-1.41421 - 1.41421i) q^{2} +(-7.12210 + 7.12210i) q^{3} +4.00000i q^{4} +(1.63222 + 11.0606i) q^{5} +20.1443 q^{6} +(16.1147 - 16.1147i) q^{7} +(5.65685 - 5.65685i) q^{8} -74.4485i q^{9} +(13.3337 - 17.9503i) q^{10} +27.4497i q^{11} +(-28.4884 - 28.4884i) q^{12} +(38.2364 - 38.2364i) q^{13} -45.5793 q^{14} +(-90.3991 - 67.1495i) q^{15} -16.0000 q^{16} +(24.6785 - 24.6785i) q^{17} +(-105.286 + 105.286i) q^{18} +142.088 q^{19} +(-44.2422 + 6.52887i) q^{20} +229.541i q^{21} +(38.8197 - 38.8197i) q^{22} +(-76.6061 - 79.3632i) q^{23} +80.5773i q^{24} +(-119.672 + 36.1065i) q^{25} -108.149 q^{26} +(337.933 + 337.933i) q^{27} +(64.4589 + 64.4589i) q^{28} +43.7471i q^{29} +(32.8799 + 222.807i) q^{30} +206.174 q^{31} +(22.6274 + 22.6274i) q^{32} +(-195.499 - 195.499i) q^{33} -69.8012 q^{34} +(204.541 + 151.935i) q^{35} +297.794 q^{36} +(62.6196 - 62.6196i) q^{37} +(-200.942 - 200.942i) q^{38} +544.647i q^{39} +(71.8012 + 53.3347i) q^{40} +104.295 q^{41} +(324.620 - 324.620i) q^{42} +(-6.53188 - 6.53188i) q^{43} -109.799 q^{44} +(823.441 - 121.516i) q^{45} +(-3.89914 + 220.574i) q^{46} +(-123.349 - 123.349i) q^{47} +(113.954 - 113.954i) q^{48} -176.369i q^{49} +(220.304 + 118.179i) q^{50} +351.525i q^{51} +(152.946 + 152.946i) q^{52} +(-414.929 - 414.929i) q^{53} -955.818i q^{54} +(-303.609 + 44.8039i) q^{55} -182.317i q^{56} +(-1011.96 + 1011.96i) q^{57} +(61.8678 - 61.8678i) q^{58} +636.533i q^{59} +(268.598 - 361.597i) q^{60} +411.285i q^{61} +(-291.573 - 291.573i) q^{62} +(-1199.72 - 1199.72i) q^{63} -64.0000i q^{64} +(485.326 + 360.506i) q^{65} +552.956i q^{66} +(154.446 - 154.446i) q^{67} +(98.7139 + 98.7139i) q^{68} +(1110.83 + 19.6364i) q^{69} +(-74.3955 - 504.133i) q^{70} +615.260 q^{71} +(-421.144 - 421.144i) q^{72} +(222.982 - 222.982i) q^{73} -177.115 q^{74} +(595.160 - 1109.47i) q^{75} +568.350i q^{76} +(442.345 + 442.345i) q^{77} +(770.247 - 770.247i) q^{78} +322.803 q^{79} +(-26.1155 - 176.969i) q^{80} -2803.47 q^{81} +(-147.495 - 147.495i) q^{82} +(940.658 + 940.658i) q^{83} -918.165 q^{84} +(313.238 + 232.677i) q^{85} +18.4749i q^{86} +(-311.571 - 311.571i) q^{87} +(155.279 + 155.279i) q^{88} -834.848 q^{89} +(-1336.37 - 992.672i) q^{90} -1232.34i q^{91} +(317.453 - 306.424i) q^{92} +(-1468.39 + 1468.39i) q^{93} +348.885i q^{94} +(231.918 + 1571.57i) q^{95} -322.309 q^{96} +(629.315 - 629.315i) q^{97} +(-249.424 + 249.424i) q^{98} +2043.59 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 16 q^{3} - 16 q^{6}+O(q^{10}) $ 72 * q - 16 * q^3 - 16 * q^6	$ 72 q - 16 q^{3} - 16 q^{6} - 64 q^{12} + 192 q^{13} - 1152 q^{16} + 32 q^{18} + 276 q^{23} + 880 q^{25} + 304 q^{26} + 728 q^{27} + 608 q^{31} + 688 q^{35} + 2816 q^{36} - 2208 q^{41} - 256 q^{46} + 144 q^{47} + 256 q^{48} + 272 q^{50} + 768 q^{52} - 2360 q^{55} - 1376 q^{62} - 1104 q^{70} + 4528 q^{71} + 128 q^{72} - 1296 q^{73} - 2568 q^{75} - 752 q^{77} + 6000 q^{78} - 11560 q^{81} + 80 q^{82} - 904 q^{85} + 6760 q^{87} + 1104 q^{92} - 5288 q^{93} + 9264 q^{95} + 256 q^{96} - 448 q^{98}+O(q^{100}) $ 72 * q - 16 * q^3 - 16 * q^6 - 64 * q^12 + 192 * q^13 - 1152 * q^16 + 32 * q^18 + 276 * q^23 + 880 * q^25 + 304 * q^26 + 728 * q^27 + 608 * q^31 + 688 * q^35 + 2816 * q^36 - 2208 * q^41 - 256 * q^46 + 144 * q^47 + 256 * q^48 + 272 * q^50 + 768 * q^52 - 2360 * q^55 - 1376 * q^62 - 1104 * q^70 + 4528 * q^71 + 128 * q^72 - 1296 * q^73 - 2568 * q^75 - 752 * q^77 + 6000 * q^78 - 11560 * q^81 + 80 * q^82 - 904 * q^85 + 6760 * q^87 + 1104 * q^92 - 5288 * q^93 + 9264 * q^95 + 256 * q^96 - 448 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.41421	−	1.41421i	−0.500000	−	0.500000i
$2$	−1.41421	−	1.41421i	−0.500000	−	0.500000i
$3$	−7.12210	+	7.12210i	−1.37065	+	1.37065i	−0.511166	+	0.859482i	$0.670786\pi$
$3$	−7.12210	+	7.12210i	−1.37065	+	1.37065i	−0.859482	+	0.511166i	$0.829214\pi$
$4$			4.00000i			0.500000i
$5$	1.63222	+	11.0606i	0.145990	+	0.989286i
$5$	1.63222	+	11.0606i	0.145990	+	0.989286i
$6$	20.1443			1.37065
$7$	16.1147	−	16.1147i	0.870114	−	0.870114i	−0.122371	−	0.992484i	$-0.539050\pi$
$7$	16.1147	−	16.1147i	0.870114	−	0.870114i	0.992484	+	0.122371i	$0.0390497\pi$
$8$	5.65685	−	5.65685i	0.250000	−	0.250000i
$9$		−	74.4485i		−	2.75735i
$10$	13.3337	−	17.9503i	0.421648	−	0.567638i
$11$			27.4497i			0.752400i	0.926539	+	0.376200i	$0.122769\pi$
$11$			27.4497i			0.752400i	−0.926539	+	0.376200i	$0.877231\pi$
$12$	−28.4884	−	28.4884i	−0.685324	−	0.685324i
$13$	38.2364	−	38.2364i	0.815759	−	0.815759i	−0.169731	−	0.985490i	$-0.554290\pi$
$13$	38.2364	−	38.2364i	0.815759	−	0.815759i	0.985490	+	0.169731i	$0.0542899\pi$
$14$	−45.5793			−0.870114
$15$	−90.3991	−	67.1495i	−1.55606	−	1.15586i
$16$	−16.0000			−0.250000
$17$	24.6785	−	24.6785i	0.352083	−	0.352083i	−0.508801	−	0.860884i	$-0.669911\pi$
$17$	24.6785	−	24.6785i	0.352083	−	0.352083i	0.860884	+	0.508801i	$0.169911\pi$
$18$	−105.286	+	105.286i	−1.37868	+	1.37868i
$19$	142.088			1.71564			0.857819	−	0.513952i	$-0.171819\pi$
$19$	142.088			1.71564			0.857819	+	0.513952i	$0.171819\pi$
$20$	−44.2422	+	6.52887i	−0.494643	+	0.0729950i
$21$			229.541i			2.38524i
$22$	38.8197	−	38.8197i	0.376200	−	0.376200i
$23$	−76.6061	−	79.3632i	−0.694499	−	0.719494i
$23$	−76.6061	−	79.3632i	−0.694499	−	0.719494i
$24$			80.5773i			0.685324i
$25$	−119.672	+	36.1065i	−0.957374	+	0.288852i
$26$	−108.149			−0.815759
$27$	337.933	+	337.933i	2.40871	+	2.40871i
$28$	64.4589	+	64.4589i	0.435057	+	0.435057i
$29$			43.7471i			0.280125i	0.990143	+	0.140063i	$0.0447304\pi$
$29$			43.7471i			0.280125i	−0.990143	+	0.140063i	$0.955270\pi$
$30$	32.8799	+	222.807i	0.200101	+	1.35596i
$31$	206.174			1.19451			0.597256	−	0.802051i	$-0.296258\pi$
$31$	206.174			1.19451			0.597256	+	0.802051i	$0.296258\pi$
$32$	22.6274	+	22.6274i	0.125000	+	0.125000i
$33$	−195.499	−	195.499i	−1.03127	−	1.03127i
$34$	−69.8012			−0.352083
$35$	204.541	+	151.935i	0.987819	+	0.733763i
$36$	297.794			1.37868
$37$	62.6196	−	62.6196i	0.278233	−	0.278233i	−0.554171	−	0.832403i	$-0.686964\pi$
$37$	62.6196	−	62.6196i	0.278233	−	0.278233i	0.832403	+	0.554171i	$0.186964\pi$
$38$	−200.942	−	200.942i	−0.857819	−	0.857819i
$39$			544.647i			2.23624i
$40$	71.8012	+	53.3347i	0.283819	+	0.210824i
$41$	104.295			0.397271			0.198636	−	0.980073i	$-0.436349\pi$
$41$	104.295			0.397271			0.198636	+	0.980073i	$0.436349\pi$
$42$	324.620	−	324.620i	1.19262	−	1.19262i
$43$	−6.53188	−	6.53188i	−0.0231652	−	0.0231652i	0.695429	−	0.718594i	$-0.255214\pi$
$43$	−6.53188	−	6.53188i	−0.0231652	−	0.0231652i	−0.718594	+	0.695429i	$0.755214\pi$
$44$	−109.799			−0.376200
$45$	823.441	−	121.516i	2.72781	−	0.402546i
$46$	−3.89914	+	220.574i	−0.0124978	+	0.706996i
$47$	−123.349	−	123.349i	−0.382816	−	0.382816i	0.489299	−	0.872116i	$-0.337253\pi$
$47$	−123.349	−	123.349i	−0.382816	−	0.382816i	−0.872116	+	0.489299i	$0.837253\pi$
$48$	113.954	−	113.954i	0.342662	−	0.342662i
$49$		−	176.369i		−	0.514196i
$50$	220.304	+	118.179i	0.623113	+	0.334261i
$51$			351.525i			0.965163i
$52$	152.946	+	152.946i	0.407880	+	0.407880i
$53$	−414.929	−	414.929i	−1.07537	−	1.07537i	−0.996918	−	0.0784570i	$-0.975001\pi$
$53$	−414.929	−	414.929i	−1.07537	−	1.07537i	−0.0784570	−	0.996918i	$-0.524999\pi$
$54$		−	955.818i		−	2.40871i
$55$	−303.609	+	44.8039i	−0.744338	+	0.109843i
$56$		−	182.317i		−	0.435057i
$57$	−1011.96	+	1011.96i	−2.35153	+	2.35153i
$58$	61.8678	−	61.8678i	0.140063	−	0.140063i
$59$			636.533i			1.40457i	0.711897	+	0.702284i	$0.247836\pi$
$59$			636.533i			1.40457i	−0.711897	+	0.702284i	$0.752164\pi$
$60$	268.598	−	361.597i	0.577931	−	0.778032i
$61$			411.285i			0.863274i	0.902047	+	0.431637i	$0.142064\pi$
$61$			411.285i			0.863274i	−0.902047	+	0.431637i	$0.857936\pi$
$62$	−291.573	−	291.573i	−0.597256	−	0.597256i
$63$	−1199.72	−	1199.72i	−2.39921	−	2.39921i
$64$		−	64.0000i		−	0.125000i
$65$	485.326	+	360.506i	0.926112	+	0.687927i
$66$			552.956i			1.03127i
$67$	154.446	−	154.446i	0.281621	−	0.281621i	−0.552134	−	0.833755i	$-0.686186\pi$
$67$	154.446	−	154.446i	0.281621	−	0.281621i	0.833755	+	0.552134i	$0.186186\pi$
$68$	98.7139	+	98.7139i	0.176041	+	0.176041i
$69$	1110.83	+	19.6364i	1.93809	+	0.0342601i
$70$	−74.3955	−	504.133i	−0.127028	−	0.860791i
$71$	615.260			1.02842			0.514210	−	0.857664i	$-0.328085\pi$
$71$	615.260			1.02842			0.514210	+	0.857664i	$0.328085\pi$
$72$	−421.144	−	421.144i	−0.689338	−	0.689338i
$73$	222.982	−	222.982i	0.357507	−	0.357507i	−0.505386	−	0.862893i	$-0.668650\pi$
$73$	222.982	−	222.982i	0.357507	−	0.357507i	0.862893	+	0.505386i	$0.168650\pi$
$74$	−177.115			−0.278233
$75$	595.160	−	1109.47i	0.916308	−	1.70814i
$76$			568.350i			0.857819i
$77$	442.345	+	442.345i	0.654673	+	0.654673i
$78$	770.247	−	770.247i	1.11812	−	1.11812i
$79$	322.803			0.459723			0.229862	−	0.973223i	$-0.426173\pi$
$79$	322.803			0.459723			0.229862	+	0.973223i	$0.426173\pi$
$80$	−26.1155	−	176.969i	−0.0364975	−	0.247322i
$81$	−2803.47			−3.84563
$82$	−147.495	−	147.495i	−0.198636	−	0.198636i
$83$	940.658	+	940.658i	1.24398	+	1.24398i	0.958334	+	0.285649i	$0.0922091\pi$
$83$	940.658	+	940.658i	1.24398	+	1.24398i	0.285649	+	0.958334i	$0.407791\pi$
$84$	−918.165			−1.19262
$85$	313.238	+	232.677i	0.399711	+	0.296910i
$86$			18.4749i			0.0231652i
$87$	−311.571	−	311.571i	−0.383953	−	0.383953i
$88$	155.279	+	155.279i	0.188100	+	0.188100i
$89$	−834.848			−0.994311			−0.497156	−	0.867661i	$-0.665622\pi$
$89$	−834.848			−0.994311			−0.497156	+	0.867661i	$0.665622\pi$
$90$	−1336.37	−	992.672i	−1.56518	−	1.16263i
$91$		−	1232.34i		−	1.41961i
$92$	317.453	−	306.424i	0.359747	−	0.347249i
$93$	−1468.39	+	1468.39i	−1.63725	+	1.63725i
$94$			348.885i			0.382816i
$95$	231.918	+	1571.57i	0.250466	+	1.69726i
$96$	−322.309			−0.342662
$97$	629.315	−	629.315i	0.658735	−	0.658735i	−0.296346	−	0.955081i	$-0.595768\pi$
$97$	629.315	−	629.315i	0.658735	−	0.658735i	0.955081	+	0.296346i	$0.0957682\pi$
$98$	−249.424	+	249.424i	−0.257098	+	0.257098i
$99$	2043.59			2.07463
$100$	−144.426	−	478.687i	−0.144426	−	0.478687i
$101$	594.387			0.585581			0.292791	−	0.956177i	$-0.405416\pi$
$101$	594.387			0.585581			0.292791	+	0.956177i	$0.405416\pi$
$102$	497.131	−	497.131i	0.482582	−	0.482582i
$103$	−710.407	−	710.407i	−0.679597	−	0.679597i	0.280312	−	0.959909i	$-0.409562\pi$
$103$	−710.407	−	710.407i	−0.679597	−	0.679597i	−0.959909	+	0.280312i	$0.909562\pi$
$104$		−	432.596i		−	0.407880i
$105$	−2538.85	+	374.662i	−2.35968	+	0.348221i
$106$			1173.60i			1.07537i
$107$	−401.339	+	401.339i	−0.362607	+	0.362607i	−0.864772	−	0.502165i	$-0.832537\pi$
$107$	−401.339	+	401.339i	−0.362607	+	0.362607i	0.502165	+	0.864772i	$0.332537\pi$
$108$	−1351.73	+	1351.73i	−1.20435	+	1.20435i
$109$	−1915.28			−1.68303			−0.841515	−	0.540234i	$-0.818336\pi$
$109$	−1915.28			−1.68303			−0.841515	+	0.540234i	$0.818336\pi$
$110$	492.730	+	366.006i	0.427091	+	0.317248i
$111$			891.966i			0.762718i
$112$	−257.836	+	257.836i	−0.217528	+	0.217528i
$113$	71.7140	+	71.7140i	0.0597016	+	0.0597016i	0.736327	−	0.676626i	$-0.236558\pi$
$113$	71.7140	+	71.7140i	0.0597016	+	0.0597016i	−0.676626	+	0.736327i	$0.736558\pi$
$114$	2862.26			2.35153
$115$	752.763	−	976.843i	0.610396	−	0.792097i
$116$	−174.989			−0.140063
$117$	−2846.64	−	2846.64i	−2.24933	−	2.24933i
$118$	900.194	−	900.194i	0.702284	−	0.702284i
$119$		−	795.374i		−	0.612704i
$120$	−891.230	+	131.520i	−0.677981	+	0.100050i
$121$	577.514			0.433895
$122$	581.645	−	581.645i	0.431637	−	0.431637i
$123$	−742.798	+	742.798i	−0.544519	+	0.544519i
$124$			824.694i			0.597256i
$125$	−594.688	−	1264.70i	−0.425524	−	0.904947i
$126$			3393.31i			2.39921i
$127$	1563.48	+	1563.48i	1.09241	+	1.09241i	0.995270	+	0.0971436i	$0.0309706\pi$
$127$	1563.48	+	1563.48i	1.09241	+	1.09241i	0.0971436	+	0.995270i	$0.469029\pi$
$128$	−90.5097	+	90.5097i	−0.0625000	+	0.0625000i
$129$	93.0413			0.0635026
$130$	−176.523	−	1196.19i	−0.119093	−	0.807019i
$131$	1046.59			0.698021			0.349011	−	0.937119i	$-0.386518\pi$
$131$	1046.59			0.698021			0.349011	+	0.937119i	$0.386518\pi$
$132$	781.997	−	781.997i	0.515637	−	0.515637i
$133$	2289.70	−	2289.70i	1.49280	−	1.49280i
$134$	−436.840			−0.281621
$135$	−3186.14	+	4289.30i	−2.03125	+	2.73455i
$136$		−	279.205i		−	0.176041i
$137$	1614.65	−	1614.65i	1.00693	−	1.00693i	0.00695156	−	0.999976i	$-0.497787\pi$
$137$	1614.65	−	1614.65i	1.00693	−	1.00693i	0.999976	−	0.00695156i	$-0.00221277\pi$
$138$	−1543.18	−	1598.72i	−0.951913	−	0.986173i
$139$		−	2547.30i		−	1.55438i	−0.629264	−	0.777192i	$-0.716643\pi$
$139$		−	2547.30i		−	1.55438i	0.629264	−	0.777192i	$-0.283357\pi$
$140$	−607.740	+	818.163i	−0.366882	+	0.493910i
$141$	1757.01			1.04941
$142$	−870.109	−	870.109i	−0.514210	−	0.514210i
$143$	1049.58	+	1049.58i	0.613777	+	0.613777i
$144$			1191.18i			0.689338i
$145$	−483.868	+	71.4049i	−0.277124	+	0.0408955i
$146$	−630.687			−0.357507
$147$	1256.12	+	1256.12i	0.704781	+	0.704781i
$148$	250.479	+	250.479i	0.139116	+	0.139116i
$149$	−638.944			−0.351304			−0.175652	−	0.984452i	$-0.556203\pi$
$149$	−638.944			−0.351304			−0.175652	+	0.984452i	$0.556203\pi$
$150$	−2410.71	+	727.341i	−1.31222	+	0.395914i
$151$	1199.61			0.646507			0.323253	−	0.946312i	$-0.395223\pi$
$151$	1199.61			0.646507			0.323253	+	0.946312i	$0.395223\pi$
$152$	803.768	−	803.768i	0.428909	−	0.428909i
$153$	−1837.27	−	1837.27i	−0.970816	−	0.970816i
$154$		−	1251.14i		−	0.654673i
$155$	336.520	+	2280.39i	0.174387	+	1.18171i
$156$	−2178.59			−1.11812
$157$	−1715.14	+	1715.14i	−0.871867	+	0.871867i	−0.992676	−	0.120809i	$-0.961451\pi$
$157$	−1715.14	+	1715.14i	−0.871867	+	0.871867i	0.120809	+	0.992676i	$0.461451\pi$
$158$	−456.512	−	456.512i	−0.229862	−	0.229862i
$159$	5910.32			2.94792
$160$	−213.339	+	287.205i	−0.105412	+	0.141910i
$161$	−2513.40	−	44.4301i	−1.23033	−	0.0217490i
$162$	3964.70	+	3964.70i	1.92282	+	1.92282i
$163$	798.401	−	798.401i	0.383654	−	0.383654i	−0.488763	−	0.872417i	$-0.662552\pi$
$163$	798.401	−	798.401i	0.383654	−	0.383654i	0.872417	+	0.488763i	$0.162552\pi$
$164$			417.179i			0.198636i
$165$	1843.23	−	2481.43i	0.869670	−	1.17078i
$166$		−	2660.58i		−	1.24398i
$167$	2100.59	+	2100.59i	0.973345	+	0.973345i	0.999654	−	0.0263085i	$-0.00837521\pi$
$167$	2100.59	+	2100.59i	0.973345	+	0.973345i	−0.0263085	+	0.999654i	$0.508375\pi$
$168$	1298.48	+	1298.48i	0.596310	+	0.596310i
$169$		−	727.046i		−	0.330927i
$170$	−113.931	−	772.041i	−0.0514006	−	0.348311i
$171$		−	10578.2i		−	4.73061i
$172$	26.1275	−	26.1275i	0.0115826	−	0.0115826i
$173$	199.997	−	199.997i	0.0878929	−	0.0878929i	−0.661793	−	0.749686i	$-0.730204\pi$
$173$	199.997	−	199.997i	0.0878929	−	0.0878929i	0.749686	+	0.661793i	$0.230204\pi$
$174$			881.257i			0.383953i
$175$	−1346.63	+	2510.32i	−0.581690	+	1.08436i
$176$		−	439.195i		−	0.188100i
$177$	−4533.45	−	4533.45i	−1.92517	−	1.92517i
$178$	1180.65	+	1180.65i	0.497156	+	0.497156i
$179$		−	1252.06i		−	0.522812i	−0.965229	−	0.261406i	$-0.915814\pi$
$179$		−	1252.06i		−	0.522812i	0.965229	−	0.261406i	$-0.0841862\pi$
$180$	486.065	+	3293.77i	0.201273	+	1.36390i
$181$		−	563.380i		−	0.231357i	−0.993287	−	0.115679i	$-0.963096\pi$
$181$		−	563.380i		−	0.231357i	0.993287	−	0.115679i	$-0.0369043\pi$
$182$	−1742.79	+	1742.79i	−0.709803	+	0.709803i
$183$	−2929.21	−	2929.21i	−1.18324	−	1.18324i
$184$	−882.295	−	15.5966i	−0.353498	−	0.00624889i
$185$	794.817	+	590.399i	0.315871	+	0.234632i
$186$	4153.23			1.63725
$187$	677.417	+	677.417i	0.264907	+	0.264907i
$188$	493.398	−	493.398i	0.191408	−	0.191408i
$189$	10891.4			4.19170
$190$	1894.55	−	2550.51i	0.723395	−	0.973861i
$191$			2269.65i			0.859823i	0.902871	+	0.429911i	$0.141455\pi$
$191$			2269.65i			0.859823i	−0.902871	+	0.429911i	$0.858545\pi$
$192$	455.814	+	455.814i	0.171331	+	0.171331i
$193$	238.862	−	238.862i	0.0890864	−	0.0890864i	−0.661159	−	0.750246i	$-0.729935\pi$
$193$	238.862	−	238.862i	0.0890864	−	0.0890864i	0.750246	+	0.661159i	$0.229935\pi$
$194$	−1779.97			−0.658735
$195$	−6024.09	+	888.982i	−2.21228	+	0.326468i
$196$	705.477			0.257098
$197$	1840.37	+	1840.37i	0.665587	+	0.665587i	0.956691	−	0.291104i	$-0.0940226\pi$
$197$	1840.37	+	1840.37i	0.665587	+	0.665587i	−0.291104	+	0.956691i	$0.594023\pi$
$198$	−2890.07	−	2890.07i	−1.03731	−	1.03731i
$199$	4404.97			1.56915			0.784574	−	0.620036i	$-0.212882\pi$
$199$	4404.97			1.56915			0.784574	+	0.620036i	$0.212882\pi$
$200$	−472.716	+	881.215i	−0.167130	+	0.311556i
$201$			2199.96i			0.772007i
$202$	−840.590	−	840.590i	−0.292791	−	0.292791i
$203$	704.973	+	704.973i	0.243741	+	0.243741i
$204$	−1406.10			−0.482582
$205$	170.232	+	1153.56i	0.0579976	+	0.393015i
$206$			2009.34i			0.679597i
$207$	−5908.47	+	5703.20i	−1.98390	+	1.91498i
$208$	−611.783	+	611.783i	−0.203940	+	0.203940i
$209$			3900.26i			1.29084i
$210$	4120.33	+	3060.63i	1.35395	+	1.00573i
$211$	2794.68			0.911818			0.455909	−	0.890027i	$-0.349314\pi$
$211$	2794.68			0.911818			0.455909	+	0.890027i	$0.349314\pi$
$212$	1659.72	−	1659.72i	0.537687	−	0.537687i
$213$	−4381.94	+	4381.94i	−1.40960	+	1.40960i
$214$	1135.16			0.362607
$215$	61.5848	−	82.9077i	0.0195351	−	0.0262989i
$216$	3823.27			1.20435
$217$	3322.43	−	3322.43i	1.03936	−	1.03936i
$218$	2708.61	+	2708.61i	0.841515	+	0.841515i
$219$			3176.19i			0.980033i
$220$	−179.216	−	1214.44i	−0.0549214	−	0.372169i
$221$		−	1887.23i		−	0.574430i
$222$	1261.43	−	1261.43i	0.381359	−	0.381359i
$223$	−4243.98	+	4243.98i	−1.27443	+	1.27443i	−0.330692	+	0.943739i	$0.607282\pi$
$223$	−4243.98	+	4243.98i	−1.27443	+	1.27443i	−0.943739	+	0.330692i	$0.892718\pi$
$224$	729.270			0.217528
$225$	2688.07	+	8909.38i	0.796466	+	2.63982i
$226$		−	202.838i		−	0.0597016i
$227$	−869.453	+	869.453i	−0.254219	+	0.254219i	−0.822698	−	0.568479i	$-0.807532\pi$
$227$	−869.453	+	869.453i	−0.254219	+	0.254219i	0.568479	+	0.822698i	$0.307532\pi$
$228$	−4047.84	−	4047.84i	−1.17577	−	1.17577i
$229$	−3180.77			−0.917865			−0.458933	−	0.888471i	$-0.651768\pi$
$229$	−3180.77			−0.917865			−0.458933	+	0.888471i	$0.651768\pi$
$230$	−2446.03	+	316.898i	−0.701246	+	0.0908506i
$231$	−6300.84			−1.79465
$232$	247.471	+	247.471i	0.0700314	+	0.0700314i
$233$	−1285.46	+	1285.46i	−0.361431	+	0.361431i	−0.864339	−	0.502909i	$-0.832263\pi$
$233$	−1285.46	+	1285.46i	−0.361431	+	0.361431i	0.502909	+	0.864339i	$0.332263\pi$
$234$			8051.52i			2.24933i
$235$	1162.98	−	1565.65i	0.322827	−	0.434602i
$236$	−2546.13			−0.702284
$237$	−2299.03	+	2299.03i	−0.630119	+	0.630119i
$238$	−1124.83	+	1124.83i	−0.306352	+	0.306352i
$239$			1527.22i			0.413337i	0.978411	+	0.206669i	$0.0662622\pi$
$239$			1527.22i			0.413337i	−0.978411	+	0.206669i	$0.933738\pi$
$240$	1446.39	+	1074.39i	0.389016	+	0.288965i
$241$			2549.54i			0.681453i	0.940162	+	0.340726i	$0.110673\pi$
$241$			2549.54i			0.681453i	−0.940162	+	0.340726i	$0.889327\pi$
$242$	−816.728	−	816.728i	−0.216947	−	0.216947i
$243$	10842.4	−	10842.4i	2.86230	−	2.86230i
$244$	−1645.14			−0.431637
$245$	1950.74	−	287.873i	0.508687	−	0.0750675i
$246$	2100.95			0.544519
$247$	5432.92	−	5432.92i	1.39955	−	1.39955i
$248$	1166.29	−	1166.29i	0.298628	−	0.298628i
$249$	−13398.9			−3.41013
$250$	−947.543	+	2629.57i	−0.239711	+	0.665236i
$251$			693.483i			0.174391i	0.996191	+	0.0871957i	$0.0277906\pi$
$251$			693.483i			0.174391i	−0.996191	+	0.0871957i	$0.972209\pi$
$252$	4798.87	−	4798.87i	1.19960	−	1.19960i
$253$	2178.50	−	2102.81i	0.541347	−	0.522540i
$254$		−	4422.19i		−	1.09241i
$255$	−3888.06	+	573.765i	−0.954822	+	0.140904i
$256$	256.000			0.0625000
$257$	808.133	+	808.133i	0.196148	+	0.196148i	0.798346	−	0.602199i	$-0.205708\pi$
$257$	808.133	+	808.133i	0.196148	+	0.196148i	−0.602199	+	0.798346i	$0.705708\pi$
$258$	−131.580	−	131.580i	−0.0317513	−	0.0317513i
$259$		−	2018.20i		−	0.484188i
$260$	−1442.02	+	1941.30i	−0.343963	+	0.463056i
$261$	3256.91			0.772404
$262$	−1480.10	−	1480.10i	−0.349011	−	0.349011i
$263$	−1549.40	−	1549.40i	−0.363270	−	0.363270i	0.501745	−	0.865015i	$-0.332691\pi$
$263$	−1549.40	−	1549.40i	−0.363270	−	0.363270i	−0.865015	+	0.501745i	$0.832691\pi$
$264$	−2211.82			−0.515637
$265$	3912.09	−	5266.60i	0.906859	−	1.22085i
$266$	−6476.26			−1.49280
$267$	5945.87	−	5945.87i	1.36285	−	1.36285i
$268$	617.785	+	617.785i	0.140811	+	0.140811i
$269$			5470.95i			1.24004i	0.784588	+	0.620018i	$0.212875\pi$
$269$			5470.95i			1.24004i	−0.784588	+	0.620018i	$0.787125\pi$
$270$	10571.9	−	1560.10i	2.38290	−	0.351648i
$271$	−2589.10			−0.580357			−0.290178	−	0.956973i	$-0.593715\pi$
$271$	−2589.10			−0.580357			−0.290178	+	0.956973i	$0.593715\pi$
$272$	−394.855	+	394.855i	−0.0880207	+	0.0880207i
$273$	8776.84	+	8776.84i	1.94578	+	1.94578i
$274$	−4566.93			−1.00693
$275$	−991.112	−	3284.95i	−0.217332	−	0.720328i
$276$	−78.5456	+	4443.31i	−0.0171300	+	0.969043i
$277$	−1429.08	−	1429.08i	−0.309983	−	0.309983i	0.534920	−	0.844903i	$-0.320342\pi$
$277$	−1429.08	−	1429.08i	−0.309983	−	0.309983i	−0.844903	+	0.534920i	$0.820342\pi$
$278$	−3602.43	+	3602.43i	−0.777192	+	0.777192i
$279$		−	15349.3i		−	3.29369i
$280$	2016.53	−	297.582i	0.430396	−	0.0635140i
$281$		−	5846.47i		−	1.24118i	−0.784136	−	0.620589i	$-0.786894\pi$
$281$		−	5846.47i		−	1.24118i	0.784136	−	0.620589i	$-0.213106\pi$
$282$	−2484.79	−	2484.79i	−0.524706	−	0.524706i
$283$	1111.39	+	1111.39i	0.233447	+	0.233447i	0.814130	−	0.580683i	$-0.197214\pi$
$283$	1111.39	+	1111.39i	0.233447	+	0.233447i	−0.580683	+	0.814130i	$0.697214\pi$
$284$			2461.04i			0.514210i
$285$	−12844.6	−	9541.11i	−2.66964	−	1.98304i
$286$		−	2968.65i		−	0.613777i
$287$	1680.68	−	1680.68i	0.345671	−	0.345671i
$288$	1684.58	−	1684.58i	0.344669	−	0.344669i
$289$			3694.95i			0.752075i
$290$	785.274	+	583.310i	0.159010	+	0.118114i
$291$			8964.08i			1.80579i
$292$	891.927	+	891.927i	0.178754	+	0.178754i
$293$	499.420	+	499.420i	0.0995783	+	0.0995783i	0.755141	−	0.655563i	$-0.227568\pi$
$293$	499.420	+	499.420i	0.0995783	+	0.0995783i	−0.655563	+	0.755141i	$0.727568\pi$
$294$		−	3552.84i		−	0.704781i
$295$	−7040.41	+	1038.96i	−1.38952	+	0.205053i
$296$		−	708.460i		−	0.139116i
$297$	−9276.15	+	9276.15i	−1.81231	+	1.81231i
$298$	903.603	+	903.603i	0.175652	+	0.175652i
$299$	−5963.70	−	105.422i	−1.15348	−	0.0203903i
$300$	4437.87	+	2380.64i	0.854068	+	0.458154i
$301$	−210.519			−0.0403127
$302$	−1696.50	−	1696.50i	−0.323253	−	0.323253i
$303$	−4233.28	+	4233.28i	−0.802626	+	0.802626i
$304$	−2273.40			−0.428909
$305$	−4549.04	+	671.308i	−0.854025	+	0.126029i
$306$			5196.60i			0.970816i
$307$	−6147.74	−	6147.74i	−1.14290	−	1.14290i	−0.987917	−	0.154983i	$-0.950468\pi$
$307$	−6147.74	−	6147.74i	−1.14290	−	1.14290i	−0.154983	−	0.987917i	$-0.549532\pi$
$308$	−1769.38	+	1769.38i	−0.327337	+	0.327337i
$309$	10119.2			1.86298
$310$	2749.05	−	3700.87i	0.503663	−	0.678050i
$311$	−8717.54			−1.58947			−0.794737	−	0.606954i	$-0.792391\pi$
$311$	−8717.54			−1.58947			−0.794737	+	0.606954i	$0.792391\pi$
$312$	3080.99	+	3080.99i	0.559059	+	0.559059i
$313$	−873.680	−	873.680i	−0.157774	−	0.157774i	0.623805	−	0.781580i	$-0.285586\pi$
$313$	−873.680	−	873.680i	−0.157774	−	0.157774i	−0.781580	+	0.623805i	$0.785586\pi$
$314$	4851.15			0.871867
$315$	11311.3	−	15227.7i	2.02324	−	2.72376i
$316$			1291.21i			0.229862i
$317$	1516.89	+	1516.89i	0.268761	+	0.268761i	0.828601	−	0.559840i	$-0.189137\pi$
$317$	1516.89	+	1516.89i	0.268761	+	0.268761i	−0.559840	+	0.828601i	$0.689137\pi$
$318$	−8358.46	−	8358.46i	−1.47396	−	1.47396i
$319$	−1200.85			−0.210766
$320$	707.875	−	104.462i	0.123661	−	0.0182488i
$321$		−	5716.75i		−	0.994013i
$322$	3491.65	+	3617.32i	0.604293	+	0.626042i
$323$	3506.50	−	3506.50i	0.604046	−	0.604046i
$324$		−	11213.9i		−	1.92282i
$325$	−3195.23	+	5956.40i	−0.545353	+	1.01662i
$326$	−2258.22			−0.383654
$327$	13640.8	−	13640.8i	2.30684	−	2.30684i
$328$	589.981	−	589.981i	0.0993178	−	0.0993178i
$329$	−3975.49			−0.666188
$330$	−6116.00	+	902.545i	−1.02023	+	0.150556i
$331$	4456.14			0.739974			0.369987	−	0.929037i	$-0.379362\pi$
$331$	4456.14			0.739974			0.369987	+	0.929037i	$0.379362\pi$
$332$	−3762.63	+	3762.63i	−0.621992	+	0.621992i
$333$	−4661.94	−	4661.94i	−0.767185	−	0.767185i
$334$		−	5941.37i		−	0.973345i
$335$	1960.35	+	1456.17i	0.319718	+	0.237490i
$336$		−	3672.66i		−	0.596310i
$337$	5656.86	−	5656.86i	0.914389	−	0.914389i	−0.0822250	−	0.996614i	$-0.526203\pi$
$337$	5656.86	−	5656.86i	0.914389	−	0.914389i	0.996614	+	0.0822250i	$0.0262026\pi$
$338$	−1028.20	+	1028.20i	−0.165463	+	0.165463i
$339$	−1021.51			−0.163660
$340$	−930.708	+	1252.95i	−0.148455	+	0.199856i
$341$			5659.40i			0.898750i
$342$	−14959.8	+	14959.8i	−2.36531	+	2.36531i
$343$	2685.21	+	2685.21i	0.422705	+	0.422705i
$344$	−73.8998			−0.0115826
$345$	1595.92	+	12318.4i	0.249048	+	1.92232i
$346$	−565.676			−0.0878929
$347$	−1132.34	−	1132.34i	−0.175179	−	0.175179i	0.614071	−	0.789251i	$-0.289531\pi$
$347$	−1132.34	−	1132.34i	−0.175179	−	0.175179i	−0.789251	+	0.614071i	$0.789531\pi$
$348$	1246.29	−	1246.29i	0.191977	−	0.191977i
$349$		−	1451.24i		−	0.222588i	−0.993788	−	0.111294i	$-0.964501\pi$
$349$		−	1451.24i		−	0.222588i	0.993788	−	0.111294i	$-0.0354995\pi$
$350$	5454.56	−	1645.71i	0.833024	−	0.251334i
$351$	25842.7			3.92985
$352$	−621.116	+	621.116i	−0.0940499	+	0.0940499i
$353$	4267.32	−	4267.32i	0.643418	−	0.643418i	−0.307976	−	0.951394i	$-0.599652\pi$
$353$	4267.32	−	4267.32i	0.643418	−	0.643418i	0.951394	+	0.307976i	$0.0996518\pi$
$354$			12822.5i			1.92517i
$355$	1004.24	+	6805.11i	0.150139	+	1.01740i
$356$		−	3339.39i		−	0.497156i
$357$	5664.73	+	5664.73i	0.839802	+	0.839802i
$358$	−1770.68	+	1770.68i	−0.261406	+	0.261406i
$359$	−7713.53			−1.13400			−0.566998	−	0.823719i	$-0.691895\pi$
$359$	−7713.53			−1.13400			−0.566998	+	0.823719i	$0.691895\pi$
$360$	3970.69	−	5345.49i	0.581316	−	0.782589i
$361$	13329.9			1.94341
$362$	−796.739	+	796.739i	−0.115679	+	0.115679i
$363$	−4113.11	+	4113.11i	−0.594717	+	0.594717i
$364$	4929.36			0.709803
$365$	2830.26	+	2102.35i	0.405869	+	0.301484i
$366$			8285.07i			1.18324i
$367$	−3849.60	+	3849.60i	−0.547541	+	0.547541i	−0.925729	−	0.378188i	$-0.876547\pi$
$367$	−3849.60	+	3849.60i	−0.547541	+	0.547541i	0.378188	+	0.925729i	$0.376547\pi$
$368$	1225.70	+	1269.81i	0.173625	+	0.179874i
$369$		−	7764.59i		−	1.09542i
$370$	−289.091	−	1958.99i	−0.0406192	−	0.275252i
$371$	−13372.9			−1.87140
$372$	−5873.55	−	5873.55i	−0.818627	−	0.818627i
$373$	7015.35	+	7015.35i	0.973837	+	0.973837i	0.999666	−	0.0258297i	$-0.00822276\pi$
$373$	7015.35	+	7015.35i	0.973837	+	0.973837i	−0.0258297	+	0.999666i	$0.508223\pi$
$374$		−	1916.02i		−	0.264907i
$375$	13242.8	+	4771.90i	1.82361	+	0.657120i
$376$	−1395.54			−0.191408
$377$	1672.73	+	1672.73i	0.228515	+	0.228515i
$378$	−15402.7	−	15402.7i	−2.09585	−	2.09585i
$379$	−8727.02			−1.18279			−0.591394	−	0.806383i	$-0.701422\pi$
$379$	−8727.02			−1.18279			−0.591394	+	0.806383i	$0.701422\pi$
$380$	−6286.27	+	927.671i	−0.848628	+	0.125233i
$381$	−22270.5			−2.99463
$382$	3209.77	−	3209.77i	0.429911	−	0.429911i
$383$	−8979.34	−	8979.34i	−1.19797	−	1.19797i	−0.974773	−	0.223198i	$-0.928350\pi$
$383$	−8979.34	−	8979.34i	−1.19797	−	1.19797i	−0.223198	−	0.974773i	$-0.571650\pi$
$384$		−	1289.24i		−	0.171331i
$385$	−4170.57	+	5614.58i	−0.552083	+	0.743235i
$386$	−675.604			−0.0890864
$387$	−486.288	+	486.288i	−0.0638745	+	0.0638745i
$388$	2517.26	+	2517.26i	0.329367	+	0.329367i
$389$	1827.07			0.238139			0.119069	−	0.992886i	$-0.462009\pi$
$389$	1827.07			0.238139			0.119069	+	0.992886i	$0.462009\pi$
$390$	9776.57	+	7262.14i	1.26937	+	0.942905i
$391$	−3849.08	−	68.0413i	−0.497843	−	0.00880050i
$392$	−997.695	−	997.695i	−0.128549	−	0.128549i
$393$	−7453.90	+	7453.90i	−0.956741	+	0.956741i
$394$		−	5205.34i		−	0.665587i
$395$	526.885	+	3570.38i	0.0671150	+	0.454798i
$396$			8174.35i			1.03731i
$397$	−10067.7	−	10067.7i	−1.27275	−	1.27275i	−0.944639	−	0.328110i	$-0.893588\pi$
$397$	−10067.7	−	10067.7i	−1.27275	−	1.27275i	−0.328110	−	0.944639i	$-0.606412\pi$
$398$	−6229.57	−	6229.57i	−0.784574	−	0.784574i
$399$			32615.0i			4.09221i
$400$	1914.75	−	577.704i	0.239343	−	0.0722130i
$401$		−	8386.66i		−	1.04441i	−0.852819	−	0.522206i	$-0.825109\pi$
$401$		−	8386.66i		−	1.04441i	0.852819	−	0.522206i	$-0.174891\pi$
$402$	3111.22	−	3111.22i	0.386004	−	0.386004i
$403$	7883.33	−	7883.33i	0.974434	−	0.974434i
$404$			2377.55i			0.292791i
$405$	−4575.87	−	31007.9i	−0.561424	−	3.80443i
$406$		−	1993.97i		−	0.243741i
$407$	1718.89	+	1718.89i	0.209342	+	0.209342i
$408$	1988.52	+	1988.52i	0.241291	+	0.241291i
$409$		−	4719.57i		−	0.570582i	−0.958441	−	0.285291i	$-0.907910\pi$
$409$		−	4719.57i		−	0.570582i	0.958441	−	0.285291i	$-0.0920902\pi$
$410$	1390.63	−	1872.12i	0.167509	−	0.225506i
$411$			22999.4i			2.76029i
$412$	2841.63	−	2841.63i	0.339799	−	0.339799i
$413$	10257.6	+	10257.6i	1.22213	+	1.22213i
$414$	16421.4	+	290.285i	1.94944	+	0.0344607i
$415$	−8868.84	+	11939.6i	−1.04905	+	1.41226i
$416$	1730.38			0.203940
$417$	18142.1	+	18142.1i	2.13051	+	2.13051i
$418$	5515.80	−	5515.80i	0.645422	−	0.645422i
$419$	8363.81			0.975177			0.487588	−	0.873074i	$-0.337877\pi$
$419$	8363.81			0.975177			0.487588	+	0.873074i	$0.337877\pi$
$420$	−1498.65	−	10155.4i	−0.174111	−	1.17984i
$421$		−	3652.00i		−	0.422773i	−0.977403	−	0.211387i	$-0.932202\pi$
$421$		−	3652.00i		−	0.422773i	0.977403	−	0.211387i	$-0.0677979\pi$
$422$	−3952.27	−	3952.27i	−0.455909	−	0.455909i
$423$	−9183.18	+	9183.18i	−1.05556	+	1.05556i
$424$	−4694.38			−0.537687
$425$	−2062.26	+	3844.37i	−0.235375	+	0.438775i
$426$	12394.0			1.40960
$427$	6627.75	+	6627.75i	0.751146	+	0.751146i
$428$	−1605.36	−	1605.36i	−0.181303	−	0.181303i
$429$	−14950.4			−1.68254
$430$	−204.343	+	30.1551i	−0.0229170	+	0.00338188i
$431$			2267.23i			0.253384i	0.991942	+	0.126692i	$0.0404359\pi$
$431$			2267.23i			0.253384i	−0.991942	+	0.126692i	$0.959564\pi$
$432$	−5406.92	−	5406.92i	−0.602177	−	0.602177i
$433$	4342.15	+	4342.15i	0.481918	+	0.481918i	0.905744	−	0.423826i	$-0.139313\pi$
$433$	4342.15	+	4342.15i	0.481918	+	0.481918i	−0.423826	+	0.905744i	$0.639313\pi$
$434$	−9397.25			−1.03936
$435$	2937.60	−	3954.70i	0.323786	−	0.435893i
$436$		−	7661.11i		−	0.841515i
$437$	−10884.8	−	11276.5i	−1.19151	−	1.23439i
$438$	4491.82	−	4491.82i	0.490017	−	0.490017i
$439$			1539.46i			0.167367i	0.996492	+	0.0836837i	$0.0266686\pi$
$439$			1539.46i			0.167367i	−0.996492	+	0.0836837i	$0.973331\pi$
$440$	−1464.02	+	1970.92i	−0.158624	+	0.213545i
$441$	−13130.4			−1.41782
$442$	−2668.95	+	2668.95i	−0.287215	+	0.287215i
$443$	−10748.9	+	10748.9i	−1.15281	+	1.15281i	−0.166820	+	0.985987i	$0.553350\pi$
$443$	−10748.9	+	10748.9i	−1.15281	+	1.15281i	−0.985987	+	0.166820i	$0.946650\pi$
$444$	−3567.86			−0.381359
$445$	−1362.65	−	9233.88i	−0.145160	−	0.983658i
$446$	12003.8			1.27443
$447$	4550.62	−	4550.62i	0.481514	−	0.481514i
$448$	−1031.34	−	1031.34i	−0.108764	−	0.108764i
$449$		−	17627.2i		−	1.85274i	−0.376620	−	0.926368i	$-0.622914\pi$
$449$		−	17627.2i		−	1.85274i	0.376620	−	0.926368i	$-0.377086\pi$
$450$	8798.25	−	16401.3i	0.921675	−	1.71814i
$451$			2862.86i			0.298907i
$452$	−286.856	+	286.856i	−0.0298508	+	0.0298508i
$453$	−8543.71	+	8543.71i	−0.886133	+	0.886133i
$454$	2459.18			0.254219
$455$	13630.4	−	2011.45i	1.40440	−	0.207248i
$456$			11449.0i			1.17577i
$457$	−281.517	+	281.517i	−0.0288158	+	0.0288158i	−0.721368	−	0.692552i	$-0.756486\pi$
$457$	−281.517	+	281.517i	−0.0288158	+	0.0288158i	0.692552	+	0.721368i	$0.256486\pi$
$458$	4498.29	+	4498.29i	0.458933	+	0.458933i
$459$	16679.3			1.69613
$460$	3907.37	+	3011.05i	0.396048	+	0.305198i
$461$	16611.2			1.67823			0.839113	−	0.543957i	$-0.183075\pi$
$461$	16611.2			1.67823			0.839113	+	0.543957i	$0.183075\pi$
$462$	8910.73	+	8910.73i	0.897326	+	0.897326i
$463$	−245.722	+	245.722i	−0.0246645	+	0.0246645i	−0.719332	−	0.694667i	$-0.755552\pi$
$463$	−245.722	+	245.722i	−0.0246645	+	0.0246645i	0.694667	+	0.719332i	$0.255552\pi$
$464$		−	699.954i		−	0.0700314i
$465$	−18637.9	−	13844.4i	−1.85874	−	1.38069i
$466$	3635.83			0.361431
$467$	1752.28	−	1752.28i	0.173631	−	0.173631i	−0.614941	−	0.788573i	$-0.710820\pi$
$467$	1752.28	−	1752.28i	0.173631	−	0.173631i	0.788573	+	0.614941i	$0.210820\pi$
$468$	11386.6	−	11386.6i	1.12467	−	1.12467i
$469$		−	4977.72i		−	0.490085i
$470$	−3858.86	+	569.456i	−0.378715	+	0.0558874i
$471$		−	24430.8i		−	2.39005i
$472$	3600.77	+	3600.77i	0.351142	+	0.351142i
$473$	179.298	−	179.298i	0.0174295	−	0.0174295i
$474$	6502.64			0.630119
$475$	−17003.9	+	5130.28i	−1.64251	+	0.495565i
$476$	3181.50			0.306352
$477$	−30890.8	+	30890.8i	−2.96518	+	2.96518i
$478$	2159.81	−	2159.81i	0.206669	−	0.206669i
$479$	−546.142			−0.0520957			−0.0260479	−	0.999661i	$-0.508292\pi$
$479$	−546.142			−0.0520957			−0.0260479	+	0.999661i	$0.508292\pi$
$480$	−526.079	−	3564.92i	−0.0500252	−	0.338991i
$481$		−	4788.70i		−	0.453942i
$482$	3605.59	−	3605.59i	0.340726	−	0.340726i
$483$	18217.1	−	17584.3i	1.71617	−	1.65655i
$484$			2310.06i			0.216947i
$485$	7987.75	+	5933.39i	0.747846	+	0.555508i
$486$	−30666.9			−2.86230
$487$	−11143.2	−	11143.2i	−1.03685	−	1.03685i	−0.999294	−	0.0375569i	$-0.988042\pi$
$487$	−11143.2	−	11143.2i	−1.03685	−	1.03685i	−0.0375569	−	0.999294i	$-0.511958\pi$
$488$	2326.58	+	2326.58i	0.215818	+	0.215818i
$489$			11372.6i			1.05171i
$490$	−3165.88	−	2351.65i	−0.291877	−	0.216810i
$491$	12847.1			1.18082			0.590410	−	0.807103i	$-0.298966\pi$
$491$	12847.1			1.18082			0.590410	+	0.807103i	$0.298966\pi$
$492$	−2971.19	−	2971.19i	−0.272259	−	0.272259i
$493$	1079.61	+	1079.61i	0.0986274	+	0.0986274i
$494$	−15366.6			−1.39955
$495$	3335.58	+	22603.2i	0.302875	+	2.05240i
$496$	−3298.78			−0.298628
$497$	9914.74	−	9914.74i	0.894843	−	0.894843i
$498$	18948.9	+	18948.9i	1.70506	+	1.70506i
$499$			8850.24i			0.793971i	0.917825	+	0.396985i	$0.129944\pi$
$499$			8850.24i			0.793971i	−0.917825	+	0.396985i	$0.870056\pi$
$500$	5058.81	−	2378.75i	0.452474	−	0.212762i
$501$	−29921.2			−2.66823
$502$	980.733	−	980.733i	0.0871957	−	0.0871957i
$503$	6795.17	+	6795.17i	0.602349	+	0.602349i	0.940935	−	0.338586i	$-0.109949\pi$
$503$	6795.17	+	6795.17i	0.602349	+	0.602349i	−0.338586	+	0.940935i	$0.609949\pi$
$504$	−13573.3			−1.19960
$505$	970.169	+	6574.25i	0.0854890	+	0.579307i
$506$	−6054.68	−	107.030i	−0.531944	−	0.00940332i
$507$	5178.09	+	5178.09i	0.453584	+	0.453584i
$508$	−6253.93	+	6253.93i	−0.546207	+	0.546207i
$509$		−	1397.99i		−	0.121738i	−0.998146	−	0.0608692i	$-0.980613\pi$
$509$		−	1397.99i		−	0.121738i	0.998146	−	0.0608692i	$-0.0193872\pi$
$510$	6309.97	+	4687.12i	0.547863	+	0.406959i
$511$		−	7186.58i		−	0.622144i
$512$	−362.039	−	362.039i	−0.0312500	−	0.0312500i
$513$	48016.0	+	48016.0i	4.13247	+	4.13247i
$514$		−	2285.74i		−	0.196148i
$515$	6697.96	−	9017.04i	0.573102	−	0.771531i
$516$			372.165i			0.0317513i
$517$	3385.91	−	3385.91i	0.288031	−	0.288031i
$518$	−2854.16	+	2854.16i	−0.242094	+	0.242094i
$519$			2848.79i			0.240940i
$520$	4784.75	−	706.090i	0.403510	−	0.0595464i
$521$		−	13557.3i		−	1.14003i	−0.821634	−	0.570016i	$-0.806937\pi$
$521$		−	13557.3i		−	1.14003i	0.821634	−	0.570016i	$-0.193063\pi$
$522$	−4605.96	−	4605.96i	−0.386202	−	0.386202i
$523$	−15261.0	−	15261.0i	−1.27594	−	1.27594i	−0.942921	−	0.333016i	$-0.891934\pi$
$523$	−15261.0	−	15261.0i	−1.27594	−	1.27594i	−0.333016	−	0.942921i	$-0.608066\pi$
$524$			4186.35i			0.349011i
$525$	−8287.93	−	27469.6i	−0.688981	−	2.28357i
$526$			4382.36i			0.363270i
$527$	5088.05	−	5088.05i	0.420567	−	0.420567i
$528$	3127.99	+	3127.99i	0.257819	+	0.257819i
$529$	−430.025	+	12159.4i	−0.0353435	+	0.999375i
$530$	−12980.6	+	1915.56i	−1.06385	+	0.156994i
$531$	47388.9			3.87289
$532$	9158.81	+	9158.81i	0.746400	+	0.746400i
$533$	3987.86	−	3987.86i	0.324078	−	0.324078i
$534$	−16817.4			−1.36285
$535$	−5094.11	−	3783.96i	−0.411659	−	0.305785i
$536$		−	1747.36i		−	0.140811i
$537$	8917.29	+	8917.29i	0.716592	+	0.716592i
$538$	7737.09	−	7737.09i	0.620018	−	0.620018i
$539$	4841.28			0.386881
$540$	−17157.2	−	12744.6i	−1.36728	−	1.01563i
$541$	4066.42			0.323159			0.161580	−	0.986860i	$-0.448341\pi$
$541$	4066.42			0.323159			0.161580	+	0.986860i	$0.448341\pi$
$542$	3661.54	+	3661.54i	0.290178	+	0.290178i
$543$	4012.44	+	4012.44i	0.317110	+	0.317110i
$544$	1116.82			0.0880207
$545$	−3126.15	−	21184.0i	−0.245706	−	1.66500i
$546$		−	24824.6i		−	1.94578i
$547$	5276.65	+	5276.65i	0.412456	+	0.412456i	0.882593	−	0.470138i	$-0.155796\pi$
$547$	5276.65	+	5276.65i	0.412456	+	0.412456i	−0.470138	+	0.882593i	$0.655796\pi$
$548$	6458.61	+	6458.61i	0.503464	+	0.503464i
$549$	30619.6			2.38035
$550$	−3243.98	+	6047.27i	−0.251498	+	0.468830i
$551$			6215.92i			0.480594i
$552$	6394.87	−	6172.71i	0.493087	−	0.475956i
$553$	5201.88	−	5201.88i	0.400012	−	0.400012i
$554$			4042.06i			0.309983i
$555$	−9865.64	+	1455.88i	−0.754546	+	0.111349i
$556$	10189.2			0.777192
$557$	−18204.5	+	18204.5i	−1.38483	+	1.38483i	−0.549009	+	0.835817i	$0.684995\pi$
$557$	−18204.5	+	18204.5i	−1.38483	+	1.38483i	−0.835817	+	0.549009i	$0.815005\pi$
$558$	−21707.2	+	21707.2i	−1.64684	+	1.64684i
$559$	−499.511			−0.0377944
$560$	−3272.65	−	2430.96i	−0.246955	−	0.183441i
$561$	−9649.25			−0.726188
$562$	−8268.15	+	8268.15i	−0.620589	+	0.620589i
$563$	−1683.12	−	1683.12i	−0.125995	−	0.125995i	0.641298	−	0.767292i	$-0.278396\pi$
$563$	−1683.12	−	1683.12i	−0.125995	−	0.125995i	−0.767292	+	0.641298i	$0.778396\pi$
$564$			7028.05i			0.524706i
$565$	−676.143	+	910.249i	−0.0503461	+	0.0677778i
$566$		−	3143.49i		−	0.233447i
$567$	−45177.1	+	45177.1i	−3.34614	+	3.34614i
$568$	3480.43	−	3480.43i	0.257105	−	0.257105i
$569$	2877.60			0.212013			0.106006	−	0.994365i	$-0.466194\pi$
$569$	2877.60			0.212013			0.106006	+	0.994365i	$0.466194\pi$
$570$	4671.83	+	31658.2i	0.343301	+	2.32634i
$571$		−	21922.7i		−	1.60672i	−0.595492	−	0.803361i	$-0.703043\pi$
$571$		−	21922.7i		−	1.60672i	0.595492	−	0.803361i	$-0.296957\pi$
$572$	−4198.31	+	4198.31i	−0.306888	+	0.306888i
$573$	−16164.7	−	16164.7i	−1.17851	−	1.17851i
$574$	−4753.69			−0.345671
$575$	12033.1	+	6731.55i	0.872722	+	0.488218i
$576$	−4764.70			−0.344669
$577$	−8211.84	−	8211.84i	−0.592484	−	0.592484i	0.345818	−	0.938302i	$-0.387602\pi$
$577$	−8211.84	−	8211.84i	−0.592484	−	0.592484i	−0.938302	+	0.345818i	$0.887602\pi$
$578$	5225.44	−	5225.44i	0.376038	−	0.376038i
$579$			3402.40i			0.244212i
$580$	−285.620	−	1935.47i	−0.0204478	−	0.138562i
$581$	30316.9			2.16481
$582$	12677.1	−	12677.1i	0.902893	−	0.902893i
$583$	11389.7	−	11389.7i	0.809111	−	0.809111i
$584$		−	2522.75i		−	0.178754i
$585$	26839.1	−	36131.8i	1.89686	−	2.55362i
$586$		−	1412.57i		−	0.0995783i
$587$	11593.9	+	11593.9i	0.815217	+	0.815217i	0.985411	−	0.170193i	$-0.0544392\pi$
$587$	11593.9	+	11593.9i	0.815217	+	0.815217i	−0.170193	+	0.985411i	$0.554439\pi$
$588$	−5024.47	+	5024.47i	−0.352391	+	0.352391i
$589$	29294.7			2.04935
$590$	11426.0	+	8487.33i	0.797287	+	0.592234i
$591$	−26214.5			−1.82457
$592$	−1001.91	+	1001.91i	−0.0695581	+	0.0695581i
$593$	2896.61	−	2896.61i	0.200590	−	0.200590i	−0.599663	−	0.800253i	$-0.704699\pi$
$593$	2896.61	−	2896.61i	0.200590	−	0.200590i	0.800253	+	0.599663i	$0.204699\pi$
$594$	26236.9			1.81231
$595$	8797.28	−	1298.22i	0.606140	−	0.0894487i
$596$		−	2555.78i		−	0.175652i
$597$	−31372.6	+	31372.6i	−2.15075	+	2.15075i
$598$	8284.86	+	8583.04i	0.566544	+	0.586934i
$599$		−	8188.84i		−	0.558576i	−0.960207	−	0.279288i	$-0.909902\pi$
$599$		−	8188.84i		−	0.558576i	0.960207	−	0.279288i	$-0.0900984\pi$
$600$	−2909.36	−	9642.83i	−0.197957	−	0.656111i
$601$	−7700.03			−0.522614			−0.261307	−	0.965256i	$-0.584153\pi$
$601$	−7700.03			−0.522614			−0.261307	+	0.965256i	$0.584153\pi$
$602$	297.719	+	297.719i	0.0201563	+	0.0201563i
$603$	−11498.3	−	11498.3i	−0.776529	−	0.776529i
$604$			4798.42i			0.323253i
$605$	942.629	+	6387.63i	0.0633443	+	0.429246i
$606$	11973.5			0.802626
$607$	13097.4	+	13097.4i	0.875793	+	0.875793i	0.993096	−	0.117303i	$-0.0374250\pi$
$607$	13097.4	+	13097.4i	0.875793	+	0.875793i	−0.117303	+	0.993096i	$0.537425\pi$
$608$	3215.07	+	3215.07i	0.214455	+	0.214455i
$609$	−10041.8			−0.668166
$610$	7382.69	+	5483.95i	0.490027	+	0.363998i
$611$	−9432.88			−0.624572
$612$	7349.10	−	7349.10i	0.485408	−	0.485408i
$613$	13107.0	+	13107.0i	0.863601	+	0.863601i	0.991754	−	0.128153i	$-0.0409049\pi$
$613$	13107.0	+	13107.0i	0.863601	+	0.863601i	−0.128153	+	0.991754i	$0.540905\pi$
$614$			17388.4i			1.14290i
$615$	−9428.16	−	7003.34i	−0.618179	−	0.459190i
$616$	5004.56			0.327337
$617$	−7020.57	+	7020.57i	−0.458084	+	0.458084i	−0.898026	−	0.439942i	$-0.854999\pi$
$617$	−7020.57	+	7020.57i	−0.458084	+	0.458084i	0.439942	+	0.898026i	$0.354999\pi$
$618$	−14310.7	−	14310.7i	−0.931489	−	0.931489i
$619$	1976.20			0.128320			0.0641602	−	0.997940i	$-0.479563\pi$
$619$	1976.20			0.128320			0.0641602	+	0.997940i	$0.479563\pi$
$620$	−9121.57	+	1346.08i	−0.590857	+	0.0871934i
$621$	931.718	−	52707.1i	0.0602070	−	3.40590i
$622$	12328.5	+	12328.5i	0.794737	+	0.794737i
$623$	−13453.3	+	13453.3i	−0.865164	+	0.865164i
$624$		−	8714.35i		−	0.559059i
$625$	13017.6	−	8641.85i	0.833129	−	0.553078i
$626$			2471.14i			0.157774i
$627$	−27778.0	−	27778.0i	−1.76929	−	1.76929i
$628$	−6860.56	−	6860.56i	−0.435934	−	0.435934i
$629$		−	3090.71i		−	0.195922i
$630$	−37531.9	+	5538.63i	−2.37350	+	0.350261i
$631$		−	11436.1i		−	0.721499i	−0.932663	−	0.360749i	$-0.882521\pi$
$631$		−	11436.1i		−	0.721499i	0.932663	−	0.360749i	$-0.117479\pi$
$632$	1826.05	−	1826.05i	0.114931	−	0.114931i
$633$	−19904.0	+	19904.0i	−1.24978	+	1.24978i
$634$		−	4290.42i		−	0.268761i
$635$	−14741.0	+	19844.9i	−0.921228	+	1.24019i
$636$			23641.3i			1.47396i
$637$	−6743.72	−	6743.72i	−0.419460	−	0.419460i
$638$	1698.25	+	1698.25i	0.105383	+	0.105383i
$639$		−	45805.1i		−	2.83572i
$640$	−1148.82	−	853.356i	−0.0709548	−	0.0527060i
$641$		−	10852.6i		−	0.668724i	−0.942445	−	0.334362i	$-0.891479\pi$
$641$		−	10852.6i		−	0.668724i	0.942445	−	0.334362i	$-0.108521\pi$
$642$	−8084.71	+	8084.71i	−0.497006	+	0.497006i
$643$	3257.21	+	3257.21i	0.199769	+	0.199769i	0.799901	−	0.600132i	$-0.204885\pi$
$643$	3257.21	+	3257.21i	0.199769	+	0.199769i	−0.600132	+	0.799901i	$0.704885\pi$
$644$	177.720	−	10053.6i	0.0108745	−	0.615167i
$645$	151.864	+	1029.09i	0.00927075	+	0.0628222i
$646$	−9917.89			−0.604046
$647$	−7351.98	−	7351.98i	−0.446733	−	0.446733i	0.447534	−	0.894267i	$-0.352302\pi$
$647$	−7351.98	−	7351.98i	−0.446733	−	0.446733i	−0.894267	+	0.447534i	$0.852302\pi$
$648$	−15858.8	+	15858.8i	−0.961408	+	0.961408i
$649$	−17472.6			−1.05680
$650$	12942.4	−	3904.88i	0.780987	−	0.235634i
$651$			47325.3i			2.84920i
$652$	3193.61	+	3193.61i	0.191827	+	0.191827i
$653$	3208.84	−	3208.84i	0.192300	−	0.192300i	−0.604389	−	0.796689i	$-0.706583\pi$
$653$	3208.84	−	3208.84i	0.192300	−	0.192300i	0.796689	+	0.604389i	$0.206583\pi$
$654$	−38582.0			−2.30684
$655$	1708.26	+	11575.8i	0.101904	+	0.690543i
$656$	−1668.72			−0.0993178
$657$	−16600.6	−	16600.6i	−0.985773	−	0.985773i
$658$	5622.19	+	5622.19i	0.333094	+	0.333094i
$659$	−7184.76			−0.424702			−0.212351	−	0.977193i	$-0.568112\pi$
$659$	−7184.76			−0.424702			−0.212351	+	0.977193i	$0.568112\pi$
$660$	9925.72	+	7372.93i	0.585391	+	0.434835i
$661$		−	9953.45i		−	0.585695i	−0.956159	−	0.292847i	$-0.905397\pi$
$661$		−	9953.45i		−	0.585695i	0.956159	−	0.292847i	$-0.0946028\pi$
$662$	−6301.93	−	6301.93i	−0.369987	−	0.369987i
$663$	13441.0	+	13441.0i	0.787341	+	0.787341i
$664$	10642.3			0.621992
$665$	29062.7	+	21588.1i	1.69474	+	1.25887i
$666$			13185.9i			0.767185i
$667$	3471.91	−	3351.30i	0.201549	−	0.194547i
$668$	−8402.37	+	8402.37i	−0.486673	+	0.486673i
$669$		−	60452.1i		−	3.49359i
$670$	−713.019	−	4831.69i	−0.0411139	−	0.278604i
$671$	−11289.7			−0.649527
$672$	−5193.93	+	5193.93i	−0.298155	+	0.298155i
$673$	−14030.7	+	14030.7i	−0.803633	+	0.803633i	−0.983661	−	0.180028i	$-0.942381\pi$
$673$	−14030.7	+	14030.7i	−0.803633	+	0.803633i	0.180028	+	0.983661i	$0.442381\pi$
$674$	−16000.0			−0.914389
$675$	−52642.5	−	28239.4i	−3.00180	−	1.61027i
$676$	2908.18			0.165463
$677$	−1618.13	+	1618.13i	−0.0918609	+	0.0918609i	−0.751544	−	0.659683i	$-0.770691\pi$
$677$	−1618.13	+	1618.13i	−0.0918609	+	0.0918609i	0.659683	+	0.751544i	$0.270691\pi$
$678$	1444.63	+	1444.63i	0.0818299	+	0.0818299i
$679$		−	20282.5i		−	1.14635i
$680$	3088.16	−	455.724i	0.174155	−	0.0257003i
$681$		−	12384.7i		−	0.696888i
$682$	8003.60	−	8003.60i	0.449375	−	0.449375i
$683$	20621.3	−	20621.3i	1.15527	−	1.15527i	0.169795	−	0.985479i	$-0.445689\pi$
$683$	20621.3	−	20621.3i	1.15527	−	1.15527i	0.985479	−	0.169795i	$-0.0543106\pi$
$684$	42312.8			2.36531
$685$	20494.4	+	15223.5i	1.14314	+	0.849138i
$686$		−	7594.92i		−	0.422705i
$687$	22653.7	−	22653.7i	1.25807	−	1.25807i
$688$	104.510	+	104.510i	0.00579129	+	0.00579129i
$689$	−31730.8			−1.75449
$690$	15163.9	−	19677.9i	0.836637	−	1.08569i
$691$	−21123.6			−1.16292			−0.581462	−	0.813574i	$-0.697519\pi$
$691$	−21123.6			−1.16292			−0.581462	+	0.813574i	$0.697519\pi$
$692$	799.987	+	799.987i	0.0439464	+	0.0439464i
$693$	32931.9	−	32931.9i	1.80516	−	1.80516i
$694$			3202.74i			0.175179i
$695$	28174.6	−	4157.75i	1.53773	−	0.226925i
$696$	−3525.03			−0.191977
$697$	2573.84	−	2573.84i	0.139872	−	0.139872i
$698$	−2052.36	+	2052.36i	−0.111294	+	0.111294i
$699$		−	18310.3i		−	0.990788i
$700$	−10041.3	−	5386.53i	−0.542179	−	0.290845i
$701$		−	4382.03i		−	0.236101i	−0.993008	−	0.118051i	$-0.962336\pi$
$701$		−	4382.03i		−	0.236101i	0.993008	−	0.118051i	$-0.0376645\pi$
$702$	−36547.0	−	36547.0i	−1.96493	−	1.96493i
$703$	8897.47	−	8897.47i	0.477346	−	0.477346i
$704$	1756.78			0.0940499
$705$	2867.83	+	19433.5i	0.153204	+	1.03817i
$706$	−12069.8			−0.643418
$707$	9578.38	−	9578.38i	0.509522	−	0.509522i
$708$	18133.8	−	18133.8i	0.962584	−	0.962584i
$709$	−20059.0			−1.06253			−0.531265	−	0.847206i	$-0.678283\pi$
$709$	−20059.0			−1.06253			−0.531265	+	0.847206i	$0.678283\pi$
$710$	8203.68	−	11044.1i	0.433632	−	0.583771i
$711$		−	24032.2i		−	1.26762i
$712$	−4722.61	+	4722.61i	−0.248578	+	0.248578i
$713$	−15794.1	−	16362.6i	−0.829587	−	0.859444i
$714$		−	16022.3i		−	0.839802i
$715$	−9895.77	+	13322.1i	−0.517596	+	0.696806i
$716$	5008.24			0.261406
$717$	−10877.0	−	10877.0i	−0.566540	−	0.566540i
$718$	10908.6	+	10908.6i	0.566998	+	0.566998i
$719$			7404.37i			0.384056i	0.981389	+	0.192028i	$0.0615064\pi$
$719$			7404.37i			0.384056i	−0.981389	+	0.192028i	$0.938494\pi$
$720$	−13175.1	+	1944.26i	−0.681952	+	0.100636i
$721$	−22896.1			−1.18265
$722$	−18851.3	−	18851.3i	−0.971706	−	0.971706i
$723$	−18158.0	−	18158.0i	−0.934032	−	0.934032i
$724$	2253.52			0.115679
$725$	−1579.56	−	5235.30i	−0.0809148	−	0.268185i
$726$	11633.6			0.594717
$727$	−8344.48	+	8344.48i	−0.425694	+	0.425694i	−0.887159	−	0.461464i	$-0.847324\pi$
$727$	−8344.48	+	8344.48i	−0.425694	+	0.425694i	0.461464	+	0.887159i	$0.347324\pi$
$728$	−6971.16	−	6971.16i	−0.354902	−	0.354902i
$729$			78747.3i			4.00078i
$730$	−1029.42	−	6975.75i	−0.0521925	−	0.353677i
$731$	−322.394			−0.0163121
$732$	11716.9	−	11716.9i	0.591622	−	0.591622i
$733$	−6122.15	−	6122.15i	−0.308495	−	0.308495i	0.535830	−	0.844326i	$-0.319999\pi$
$733$	−6122.15	−	6122.15i	−0.308495	−	0.308495i	−0.844326	+	0.535830i	$0.819999\pi$
$734$	10888.3			0.547541
$735$	−11843.1	+	15943.6i	−0.594339	+	0.800122i
$736$	62.3863	−	3529.18i	0.00312444	−	0.176749i
$737$	4239.51	+	4239.51i	0.211892	+	0.211892i
$738$	−10980.8	+	10980.8i	−0.547708	+	0.547708i
$739$			27560.2i			1.37188i	0.727658	+	0.685941i	$0.240609\pi$
$739$			27560.2i			1.37188i	−0.727658	+	0.685941i	$0.759391\pi$
$740$	−2361.60	+	3179.27i	−0.117316	+	0.157935i
$741$			77387.5i			3.83657i
$742$	18912.2	+	18912.2i	0.935698	+	0.935698i
$743$	−22335.7	−	22335.7i	−1.10285	−	1.10285i	−0.994065	−	0.108785i	$-0.965304\pi$
$743$	−22335.7	−	22335.7i	−1.10285	−	1.10285i	−0.108785	−	0.994065i	$-0.534696\pi$
$744$			16612.9i			0.818627i
$745$	−1042.90	−	7067.08i	−0.0512869	−	0.347540i
$746$		−	19842.4i		−	0.973837i
$747$	70030.5	−	70030.5i	3.43010	−	3.43010i
$748$	−2709.67	+	2709.67i	−0.132453	+	0.132453i
$749$			12935.0i			0.631019i
$750$	−11979.6	−	25476.6i	−0.583244	−	1.24036i
$751$			13319.2i			0.647172i	0.946199	+	0.323586i	$0.104888\pi$
$751$			13319.2i			0.647172i	−0.946199	+	0.323586i	$0.895112\pi$
$752$	1973.59	+	1973.59i	0.0957041	+	0.0957041i
$753$	−4939.05	−	4939.05i	−0.239029	−	0.239029i
$754$		−	4731.20i		−	0.228515i
$755$	1958.02	+	13268.3i	0.0943836	+	0.639580i
$756$			43565.5i			2.09585i
$757$	6820.01	−	6820.01i	0.327447	−	0.327447i	−0.524168	−	0.851615i	$-0.675624\pi$
$757$	6820.01	−	6820.01i	0.327447	−	0.327447i	0.851615	+	0.524168i	$0.175624\pi$
$758$	12341.9	+	12341.9i	0.591394	+	0.591394i
$759$	−539.014	+	30491.9i	−0.0257773	+	1.45822i
$760$	10202.0	+	7578.20i	0.486931	+	0.361698i
$761$	18482.1			0.880386			0.440193	−	0.897903i	$-0.354910\pi$
$761$	18482.1			0.880386			0.440193	+	0.897903i	$0.354910\pi$
$762$	31495.3	+	31495.3i	1.49731	+	1.49731i
$763$	−30864.2	+	30864.2i	−1.46443	+	1.46443i
$764$	−9078.60			−0.429911
$765$	17322.4	−	23320.1i	0.818685	−	1.10214i
$766$			25397.4i			1.19797i
$767$	24338.7	+	24338.7i	1.14579	+	1.14579i
$768$	−1823.26	+	1823.26i	−0.0856655	+	0.0856655i
$769$	−14731.9			−0.690829			−0.345415	−	0.938450i	$-0.612262\pi$
$769$	−14731.9			−0.690829			−0.345415	+	0.938450i	$0.612262\pi$
$770$	13838.3	−	2042.13i	0.647659	−	0.0955758i
$771$	−11511.2			−0.537699
$772$	955.449	+	955.449i	0.0445432	+	0.0445432i
$773$	−24216.3	−	24216.3i	−1.12678	−	1.12678i	−0.990698	−	0.136080i	$-0.956549\pi$
$773$	−24216.3	−	24216.3i	−1.12678	−	1.12678i	−0.136080	−	0.990698i	$-0.543451\pi$
$774$	1375.43			0.0638745
$775$	−24673.1	+	7444.20i	−1.14359	+	0.345037i
$776$		−	7119.89i		−	0.329367i
$777$	14373.8	+	14373.8i	0.663651	+	0.663651i
$778$	−2583.86	−	2583.86i	−0.119069	−	0.119069i
$779$	14819.0			0.681573
$780$	−3555.93	−	24096.4i	−0.163234	−	1.10614i
$781$			16888.7i			0.773784i
$782$	5347.20	+	5539.65i	0.244521	+	0.253322i
$783$	−14783.6	+	14783.6i	−0.674741	+	0.674741i
$784$			2821.91i			0.128549i
$785$	−21769.9	−	16170.9i	−0.989810	−	0.735242i
$786$	21082.8			0.956741
$787$	15912.2	−	15912.2i	0.720722	−	0.720722i	−0.248030	−	0.968752i	$-0.579783\pi$
$787$	15912.2	−	15912.2i	0.720722	−	0.720722i	0.968752	+	0.248030i	$0.0797832\pi$
$788$	−7361.47	+	7361.47i	−0.332794	+	0.332794i
$789$	22069.9			0.995830
$790$	4304.15	−	5794.40i	0.193841	−	0.260956i
$791$	2311.30			0.103894
$792$	11560.3	−	11560.3i	0.518657	−	0.518657i
$793$	15726.1	+	15726.1i	0.704224	+	0.704224i
$794$			28475.7i			1.27275i
$795$	9646.94	+	65371.5i	0.430367	+	2.91634i
$796$			17619.9i			0.784574i
$797$	148.052	−	148.052i	0.00658001	−	0.00658001i	−0.703809	−	0.710389i	$-0.748519\pi$
$797$	148.052	−	148.052i	0.00658001	−	0.00658001i	0.710389	+	0.703809i	$0.248519\pi$
$798$	46124.5	−	46124.5i	2.04610	−	2.04610i
$799$	−6088.15			−0.269566
$800$	−3524.86	−	1890.87i	−0.155778	−	0.0835652i
$801$			62153.2i			2.74166i
$802$	−11860.5	+	11860.5i	−0.522206	+	0.522206i
$803$	6120.78	+	6120.78i	0.268988	+	0.268988i
$804$	−8799.85			−0.386004
$805$	−3611.00	−	27872.1i	−0.158101	−	1.22033i
$806$	−22297.4			−0.974434
$807$	−38964.6	−	38964.6i	−1.69965	−	1.69965i
$808$	3362.36	−	3362.36i	0.146395	−	0.146395i
$809$			5688.22i			0.247203i	0.992332	+	0.123601i	$0.0394444\pi$
$809$			5688.22i			0.247203i	−0.992332	+	0.123601i	$0.960556\pi$
$810$	−37380.5	+	50323.0i	−1.62150	+	2.18293i
$811$	−28963.2			−1.25405			−0.627025	−	0.778999i	$-0.715728\pi$
$811$	−28963.2			−1.25405			−0.627025	+	0.778999i	$0.715728\pi$
$812$	−2819.89	+	2819.89i	−0.121871	+	0.121871i
$813$	18439.8	−	18439.8i	0.795465	−	0.795465i
$814$		−	4861.76i		−	0.209342i
$815$	10133.9	+	7527.60i	0.435553	+	0.323534i
$816$		−	5624.40i		−	0.241291i
$817$	−928.098	−	928.098i	−0.0397430	−	0.0397430i
$818$	−6674.48	+	6674.48i	−0.285291	+	0.285291i
$819$	−91745.8			−3.91435
$820$	−4614.23	+	680.928i	−0.196507	+	0.0289988i
$821$	35532.6			1.51047			0.755236	−	0.655453i	$-0.227522\pi$
$821$	35532.6			1.51047			0.755236	+	0.655453i	$0.227522\pi$
$822$	32526.1	−	32526.1i	1.38014	−	1.38014i
$823$	−21930.8	+	21930.8i	−0.928869	+	0.928869i	−0.997633	−	0.0687636i	$-0.978095\pi$
$823$	−21930.8	+	21930.8i	−0.928869	+	0.928869i	0.0687636	+	0.997633i	$0.478095\pi$
$824$	−8037.34			−0.339799
$825$	30454.5	+	16337.0i	1.28520	+	0.689430i
$826$		−	29012.8i		−	1.22213i
$827$	−12983.0	+	12983.0i	−0.545905	+	0.545905i	−0.925254	−	0.379349i	$-0.876148\pi$
$827$	−12983.0	+	12983.0i	−0.545905	+	0.545905i	0.379349	+	0.925254i	$0.376148\pi$
$828$	−22812.8	−	23633.9i	−0.957488	−	0.991949i
$829$		−	7372.62i		−	0.308880i	−0.988002	−	0.154440i	$-0.950643\pi$
$829$		−	7372.62i		−	0.308880i	0.988002	−	0.154440i	$-0.0493574\pi$
$830$	29427.5	−	4342.65i	1.23066	−	0.181609i
$831$	20356.1			0.849756
$832$	−2447.13	−	2447.13i	−0.101970	−	0.101970i
$833$	−4352.52	−	4352.52i	−0.181040	−	0.181040i
$834$		−	51313.7i		−	2.13051i
$835$	−19805.1	+	26662.3i	−0.820818	+	1.10502i
$836$	−15601.0			−0.645422
$837$	69672.7	+	69672.7i	2.87723	+	2.87723i
$838$	−11828.2	−	11828.2i	−0.487588	−	0.487588i
$839$	15101.2			0.621394			0.310697	−	0.950509i	$-0.399437\pi$
$839$	15101.2			0.621394			0.310697	+	0.950509i	$0.399437\pi$
$840$	−12242.5	+	16481.3i	−0.502866	+	0.676976i
$841$	22475.2			0.921530
$842$	−5164.71	+	5164.71i	−0.211387	+	0.211387i
$843$	41639.1	+	41639.1i	1.70122	+	1.70122i
$844$			11178.7i			0.455909i
$845$	8041.53	−	1186.70i	0.327381	−	0.0483120i
$846$	25974.0			1.05556
$847$	9306.48	−	9306.48i	0.377538	−	0.377538i
$848$	6638.86	+	6638.86i	0.268844	+	0.268844i
$849$	−15830.9			−0.639946
$850$	8353.24	−	2520.28i	0.337075	−	0.101700i
$851$	−9766.74	−	172.649i	−0.393419	−	0.00695457i
$852$	−17527.8	−	17527.8i	−0.704801	−	0.704801i
$853$	22529.0	−	22529.0i	0.904310	−	0.904310i	−0.0914951	−	0.995806i	$-0.529165\pi$
$853$	22529.0	−	22529.0i	0.904310	−	0.904310i	0.995806	+	0.0914951i	$0.0291646\pi$
$854$		−	18746.1i		−	0.751146i
$855$	117001.	−	17265.9i	4.67993	−	0.690623i
$856$			4540.64i			0.181303i
$857$	15017.6	+	15017.6i	0.598591	+	0.598591i	0.939938	−	0.341346i	$-0.110883\pi$
$857$	15017.6	+	15017.6i	0.598591	+	0.598591i	−0.341346	+	0.939938i	$0.610883\pi$
$858$	21143.0	+	21143.0i	0.841272	+	0.841272i
$859$			130.538i			0.00518500i	0.999997	+	0.00259250i	$0.000825219\pi$
$859$			130.538i			0.00518500i	−0.999997	+	0.00259250i	$0.999175\pi$
$860$	331.631	+	246.339i	0.0131494	+	0.00976755i
$861$			23940.0i			0.947586i
$862$	3206.34	−	3206.34i	0.126692	−	0.126692i
$863$	−3873.97	+	3873.97i	−0.152806	+	0.152806i	−0.779370	−	0.626564i	$-0.784461\pi$
$863$	−3873.97	+	3873.97i	−0.152806	+	0.152806i	0.626564	+	0.779370i	$0.284461\pi$
$864$			15293.1i			0.602177i
$865$	2538.51	+	1885.64i	0.0997827	+	0.0741197i
$866$		−	12281.4i		−	0.481918i
$867$	−26315.8	−	26315.8i	−1.03083	−	1.03083i
$868$	13289.7	+	13289.7i	0.519680	+	0.519680i
$869$			8860.84i			0.345896i
$870$	−9747.19	+	1438.40i	−0.379840	+	0.0560534i
$871$		−	11810.9i		−	0.459470i
$872$	−10834.4	+	10834.4i	−0.420757	+	0.420757i
$873$	−46851.5	−	46851.5i	−1.81636	−	1.81636i
$874$	−554.020	+	31340.8i	−0.0214416	+	1.21295i
$875$	−29963.6	−	10797.1i	−1.15766	−	0.417152i
$876$	−12704.8			−0.490017
$877$	2662.35	+	2662.35i	0.102510	+	0.102510i	0.756502	−	0.653992i	$-0.226907\pi$
$877$	2662.35	+	2662.35i	0.102510	+	0.102510i	−0.653992	+	0.756502i	$0.726907\pi$
$878$	2177.12	−	2177.12i	0.0836837	−	0.0836837i
$879$	−7113.83			−0.272973
$880$	4857.74	−	716.862i	0.186085	−	0.0274607i
$881$			4486.77i			0.171581i	0.996313	+	0.0857907i	$0.0273416\pi$
$881$			4486.77i			0.171581i	−0.996313	+	0.0857907i	$0.972658\pi$
$882$	18569.2	+	18569.2i	0.708909	+	0.708909i
$883$	−11159.1	+	11159.1i	−0.425292	+	0.425292i	−0.887021	−	0.461729i	$-0.847229\pi$
$883$	−11159.1	+	11159.1i	−0.425292	+	0.425292i	0.461729	+	0.887021i	$0.347229\pi$
$884$	7548.93			0.287215
$885$	42742.9	−	57542.0i	1.62349	−	2.18560i
$886$	30402.4			1.15281
$887$	−25985.2	−	25985.2i	−0.983649	−	0.983649i	0.0162191	−	0.999868i	$-0.494837\pi$
$887$	−25985.2	−	25985.2i	−0.983649	−	0.983649i	−0.999868	+	0.0162191i	$0.994837\pi$
$888$	5045.72	+	5045.72i	0.190679	+	0.190679i
$889$	50390.2			1.90105
$890$	−11131.6	+	14985.8i	−0.419249	+	0.564409i
$891$		−	76954.3i		−	2.89345i
$892$	−16975.9	−	16975.9i	−0.637215	−	0.637215i
$893$	−17526.4	−	17526.4i	−0.656774	−	0.656774i
$894$	−12871.1			−0.481514
$895$	13848.5	−	2043.64i	0.517211	−	0.0763254i
$896$			2917.08i			0.108764i
$897$	43224.9	−	41723.2i	1.60896	−	1.55306i
$898$	−24928.6	+	24928.6i	−0.926368	+	0.926368i
$899$			9019.50i			0.334613i
$900$	−35637.5	+	10752.3i	−1.31991	+	0.398233i
$901$	−20479.6			−0.757242
$902$	4048.70	−	4048.70i	0.149453	−	0.149453i
$903$	1499.34	−	1499.34i	0.0552545	−	0.0552545i
$904$	811.351			0.0298508
$905$	6231.29	−	919.559i	0.228879	−	0.0337759i
$906$	24165.2			0.886133
$907$	−33889.7	+	33889.7i	−1.24067	+	1.24067i	−0.280947	+	0.959723i	$0.590648\pi$
$907$	−33889.7	+	33889.7i	−1.24067	+	1.24067i	−0.959723	+	0.280947i	$0.909352\pi$
$908$	−3477.81	−	3477.81i	−0.127109	−	0.127109i
$909$		−	44251.2i		−	1.61465i
$910$	−22120.8	−	16431.6i	−0.805823	−	0.598574i
$911$			22624.4i			0.822811i	0.911452	+	0.411406i	$0.134962\pi$
$911$			22624.4i			0.822811i	−0.911452	+	0.411406i	$0.865038\pi$
$912$	16191.4	−	16191.4i	0.587884	−	0.587884i
$913$	−25820.8	+	25820.8i	−0.935972	+	0.935972i
$914$	796.251			0.0288158
$915$	27617.6	−	37179.8i	0.997825	−	1.34331i
$916$		−	12723.1i		−	0.458933i
$917$	16865.5	−	16865.5i	0.607358	−	0.607358i
$918$	−23588.1	−	23588.1i	−0.848065	−	0.848065i
$919$	−6966.08			−0.250043			−0.125022	−	0.992154i	$-0.539900\pi$
$919$	−6966.08			−0.250043			−0.125022	+	0.992154i	$0.539900\pi$
$920$	−1267.59	−	9784.13i	−0.0454253	−	0.350623i
$921$	87569.6			3.13303
$922$	−23491.8	−	23491.8i	−0.839113	−	0.839113i
$923$	23525.3	−	23525.3i	0.838944	−	0.838944i
$924$		−	25203.4i		−	0.897326i
$925$	−5232.83	+	9754.77i	−0.186005	+	0.346741i
$926$	695.008			0.0246645
$927$	−52888.8	+	52888.8i	−1.87389	+	1.87389i
$928$	−989.885	+	989.885i	−0.0350157	+	0.0350157i
$929$			18244.3i			0.644322i	0.946685	+	0.322161i	$0.104409\pi$
$929$			18244.3i			0.644322i	−0.946685	+	0.322161i	$0.895591\pi$
$930$	6778.97	+	45937.0i	0.239023	+	1.61971i
$931$		−	25059.9i		−	0.882174i
$932$	−5141.84	−	5141.84i	−0.180715	−	0.180715i
$933$	62087.2	−	62087.2i	2.17861	−	2.17861i
$934$	−4956.20			−0.173631
$935$	−6386.91	+	8598.29i	−0.223395	+	0.300743i
$936$	−32206.1			−1.12467
$937$	9381.98	−	9381.98i	0.327103	−	0.327103i	−0.524381	−	0.851484i	$-0.675703\pi$
$937$	9381.98	−	9381.98i	0.327103	−	0.327103i	0.851484	+	0.524381i	$0.175703\pi$
$938$	−7039.56	+	7039.56i	−0.245043	+	0.245043i
$939$	12444.9			0.432506
$940$	6262.59	+	4651.92i	0.217301	+	0.161414i
$941$			7731.67i			0.267848i	0.990992	+	0.133924i	$0.0427579\pi$
$941$			7731.67i			0.267848i	−0.990992	+	0.133924i	$0.957242\pi$
$942$	−34550.4	+	34550.4i	−1.19502	+	1.19502i
$943$	−7989.61	−	8277.17i	−0.275904	−	0.285834i
$944$		−	10184.5i		−	0.351142i
$945$	17777.1	+	120465.i	0.611947	+	4.14679i
$946$	−507.132			−0.0174295
$947$	17602.2	+	17602.2i	0.604005	+	0.604005i	0.941373	−	0.337368i	$-0.109537\pi$
$947$	17602.2	+	17602.2i	0.604005	+	0.604005i	−0.337368	+	0.941373i	$0.609537\pi$
$948$	−9196.13	−	9196.13i	−0.315059	−	0.315059i
$949$		−	17052.0i		−	0.583280i
$950$	31302.4	+	16791.8i	1.06904	+	0.573471i
$951$	−21606.9			−0.736753
$952$	−4499.31	−	4499.31i	−0.153176	−	0.153176i
$953$	−30557.8	−	30557.8i	−1.03868	−	1.03868i	−0.999221	−	0.0394627i	$-0.987435\pi$
$953$	−30557.8	−	30557.8i	−1.03868	−	1.03868i	−0.0394627	−	0.999221i	$-0.512565\pi$
$954$	87372.4			2.96518
$955$	−25103.6	+	3704.57i	−0.850611	+	0.125526i
$956$	−6108.87			−0.206669
$957$	8552.54	−	8552.54i	0.288886	−	0.288886i
$958$	772.361	+	772.361i	0.0260479	+	0.0260479i
$959$		−	52039.4i		−	1.75228i
$960$	−4297.57	+	5785.54i	−0.144483	+	0.194508i
$961$	12716.5			0.426858
$962$	−6772.24	+	6772.24i	−0.226971	+	0.226971i
$963$	29879.1	+	29879.1i	0.999834	+	0.999834i
$964$	−10198.1			−0.340726
$965$	3031.82	+	2252.07i	0.101138	+	0.0751262i
$966$	−50630.8	−	895.015i	−1.68636	−	0.0298102i
$967$	28110.4	+	28110.4i	0.934817	+	0.934817i	0.998002	−	0.0631847i	$-0.0201257\pi$
$967$	28110.4	+	28110.4i	0.934817	+	0.934817i	−0.0631847	+	0.998002i	$0.520126\pi$
$968$	3266.91	−	3266.91i	0.108474	−	0.108474i
$969$			49947.3i			1.65587i
$970$	−2905.30	−	19687.5i	−0.0961687	−	0.651677i
$971$		−	28036.9i		−	0.926619i	−0.886197	−	0.463309i	$-0.846662\pi$
$971$		−	28036.9i		−	0.926619i	0.886197	−	0.463309i	$-0.153338\pi$
$972$	43369.5	+	43369.5i	1.43115	+	1.43115i
$973$	−41049.1	−	41049.1i	−1.35249	−	1.35249i
$974$			31517.7i			1.03685i
$975$	−19665.3	−	65178.8i	−0.645941	−	2.14092i
$976$		−	6580.57i		−	0.215818i
$977$	−31505.5	+	31505.5i	−1.03168	+	1.03168i	−0.0321964	+	0.999482i	$0.510250\pi$
$977$	−31505.5	+	31505.5i	−1.03168	+	1.03168i	−0.999482	+	0.0321964i	$0.989750\pi$
$978$	16083.3	−	16083.3i	0.525855	−	0.525855i
$979$		−	22916.3i		−	0.748119i
$980$	1151.49	+	7802.96i	0.0375337	+	0.254343i
$981$			142589.i			4.64070i
$982$	−18168.6	−	18168.6i	−0.590410	−	0.590410i
$983$	−10769.2	−	10769.2i	−0.349426	−	0.349426i	0.510470	−	0.859896i	$-0.329472\pi$
$983$	−10769.2	−	10769.2i	−0.349426	−	0.349426i	−0.859896	+	0.510470i	$0.829472\pi$
$984$			8403.79i			0.272259i
$985$	−17351.6	+	23359.4i	−0.561287	+	0.755625i
$986$		−	3053.60i		−	0.0986274i
$987$	28313.8	−	28313.8i	0.913108	−	0.913108i
$988$	21731.7	+	21731.7i	0.699774	+	0.699774i
$989$	−18.0091	+	1018.77i	−0.000579026	+	0.0327554i
$990$	27248.6	−	36683.0i	0.874763	−	1.17764i
$991$	−16400.5			−0.525710			−0.262855	−	0.964835i	$-0.584664\pi$
$991$	−16400.5			−0.525710			−0.262855	+	0.964835i	$0.584664\pi$
$992$	4665.17	+	4665.17i	0.149314	+	0.149314i
$993$	−31737.0	+	31737.0i	−1.01424	+	1.01424i
$994$	−28043.1			−0.894843
$995$	7189.88	+	48721.4i	0.229080	+	1.55234i
$996$		−	53595.6i		−	1.70506i
$997$	3317.73	+	3317.73i	0.105390	+	0.105390i	0.757835	−	0.652446i	$-0.226257\pi$
$997$	3317.73	+	3317.73i	0.105390	+	0.105390i	−0.652446	+	0.757835i	$0.726257\pi$
$998$	12516.1	−	12516.1i	0.396985	−	0.396985i
$999$	42322.4			1.34036

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.4.e.a.137.2	yes	72
5.3	odd	4	inner	230.4.e.a.183.1	yes	72
23.22	odd	2	inner	230.4.e.a.137.1	✓	72
115.68	even	4	inner	230.4.e.a.183.2	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.e.a.137.1	✓	72	23.22	odd	2	inner
230.4.e.a.137.2	yes	72	1.1	even	1	trivial
230.4.e.a.183.1	yes	72	5.3	odd	4	inner
230.4.e.a.183.2	yes	72	115.68	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	230.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41421 - 1.41421i) q^{2} +(-7.12210 + 7.12210i) q^{3} +4.00000i q^{4} +(1.63222 + 11.0606i) q^{5} +20.1443 q^{6} +(16.1147 - 16.1147i) q^{7} +(5.65685 - 5.65685i) q^{8} -74.4485i q^{9} +O(q^{10})\)	\(q+(-1.41421 - 1.41421i) q^{2} +(-7.12210 + 7.12210i) q^{3} +4.00000i q^{4} +(1.63222 + 11.0606i) q^{5} +20.1443 q^{6} +(16.1147 - 16.1147i) q^{7} +(5.65685 - 5.65685i) q^{8} -74.4485i q^{9} +(13.3337 - 17.9503i) q^{10} +27.4497i q^{11} +(-28.4884 - 28.4884i) q^{12} +(38.2364 - 38.2364i) q^{13} -45.5793 q^{14} +(-90.3991 - 67.1495i) q^{15} -16.0000 q^{16} +(24.6785 - 24.6785i) q^{17} +(-105.286 + 105.286i) q^{18} +142.088 q^{19} +(-44.2422 + 6.52887i) q^{20} +229.541i q^{21} +(38.8197 - 38.8197i) q^{22} +(-76.6061 - 79.3632i) q^{23} +80.5773i q^{24} +(-119.672 + 36.1065i) q^{25} -108.149 q^{26} +(337.933 + 337.933i) q^{27} +(64.4589 + 64.4589i) q^{28} +43.7471i q^{29} +(32.8799 + 222.807i) q^{30} +206.174 q^{31} +(22.6274 + 22.6274i) q^{32} +(-195.499 - 195.499i) q^{33} -69.8012 q^{34} +(204.541 + 151.935i) q^{35} +297.794 q^{36} +(62.6196 - 62.6196i) q^{37} +(-200.942 - 200.942i) q^{38} +544.647i q^{39} +(71.8012 + 53.3347i) q^{40} +104.295 q^{41} +(324.620 - 324.620i) q^{42} +(-6.53188 - 6.53188i) q^{43} -109.799 q^{44} +(823.441 - 121.516i) q^{45} +(-3.89914 + 220.574i) q^{46} +(-123.349 - 123.349i) q^{47} +(113.954 - 113.954i) q^{48} -176.369i q^{49} +(220.304 + 118.179i) q^{50} +351.525i q^{51} +(152.946 + 152.946i) q^{52} +(-414.929 - 414.929i) q^{53} -955.818i q^{54} +(-303.609 + 44.8039i) q^{55} -182.317i q^{56} +(-1011.96 + 1011.96i) q^{57} +(61.8678 - 61.8678i) q^{58} +636.533i q^{59} +(268.598 - 361.597i) q^{60} +411.285i q^{61} +(-291.573 - 291.573i) q^{62} +(-1199.72 - 1199.72i) q^{63} -64.0000i q^{64} +(485.326 + 360.506i) q^{65} +552.956i q^{66} +(154.446 - 154.446i) q^{67} +(98.7139 + 98.7139i) q^{68} +(1110.83 + 19.6364i) q^{69} +(-74.3955 - 504.133i) q^{70} +615.260 q^{71} +(-421.144 - 421.144i) q^{72} +(222.982 - 222.982i) q^{73} -177.115 q^{74} +(595.160 - 1109.47i) q^{75} +568.350i q^{76} +(442.345 + 442.345i) q^{77} +(770.247 - 770.247i) q^{78} +322.803 q^{79} +(-26.1155 - 176.969i) q^{80} -2803.47 q^{81} +(-147.495 - 147.495i) q^{82} +(940.658 + 940.658i) q^{83} -918.165 q^{84} +(313.238 + 232.677i) q^{85} +18.4749i q^{86} +(-311.571 - 311.571i) q^{87} +(155.279 + 155.279i) q^{88} -834.848 q^{89} +(-1336.37 - 992.672i) q^{90} -1232.34i q^{91} +(317.453 - 306.424i) q^{92} +(-1468.39 + 1468.39i) q^{93} +348.885i q^{94} +(231.918 + 1571.57i) q^{95} -322.309 q^{96} +(629.315 - 629.315i) q^{97} +(-249.424 + 249.424i) q^{98} +2043.59 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 16 q^{3} - 16 q^{6}+O(q^{10}) \) 72 * q - 16 * q^3 - 16 * q^6	\( 72 q - 16 q^{3} - 16 q^{6} - 64 q^{12} + 192 q^{13} - 1152 q^{16} + 32 q^{18} + 276 q^{23} + 880 q^{25} + 304 q^{26} + 728 q^{27} + 608 q^{31} + 688 q^{35} + 2816 q^{36} - 2208 q^{41} - 256 q^{46} + 144 q^{47} + 256 q^{48} + 272 q^{50} + 768 q^{52} - 2360 q^{55} - 1376 q^{62} - 1104 q^{70} + 4528 q^{71} + 128 q^{72} - 1296 q^{73} - 2568 q^{75} - 752 q^{77} + 6000 q^{78} - 11560 q^{81} + 80 q^{82} - 904 q^{85} + 6760 q^{87} + 1104 q^{92} - 5288 q^{93} + 9264 q^{95} + 256 q^{96} - 448 q^{98}+O(q^{100}) \) 72 * q - 16 * q^3 - 16 * q^6 - 64 * q^12 + 192 * q^13 - 1152 * q^16 + 32 * q^18 + 276 * q^23 + 880 * q^25 + 304 * q^26 + 728 * q^27 + 608 * q^31 + 688 * q^35 + 2816 * q^36 - 2208 * q^41 - 256 * q^46 + 144 * q^47 + 256 * q^48 + 272 * q^50 + 768 * q^52 - 2360 * q^55 - 1376 * q^62 - 1104 * q^70 + 4528 * q^71 + 128 * q^72 - 1296 * q^73 - 2568 * q^75 - 752 * q^77 + 6000 * q^78 - 11560 * q^81 + 80 * q^82 - 904 * q^85 + 6760 * q^87 + 1104 * q^92 - 5288 * q^93 + 9264 * q^95 + 256 * q^96 - 448 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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