LMFDB - Embedded newform 304.4.i.d.273.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,4,Mod(49,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("304.49");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	304.i (of order $3$, degree $2$, 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:	$17.9365806417$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{73})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 19x^{2} + 18x + 324 $ x^4 - x^3 + 19x^2 + 18x + 324
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			273.1
Root			$-1.88600 + 3.26665i$ of defining polynomial
Character	$\chi$	$=$	304.273
Dual form			304.4.i.d.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{3} +(-6.88600 - 11.9269i) q^{5} -27.0880 q^{7} +(13.0000 - 22.5167i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{3} +(-6.88600 - 11.9269i) q^{5} -27.0880 q^{7} +(13.0000 - 22.5167i) q^{9} +3.68399 q^{11} +(-14.5700 + 25.2360i) q^{13} +(6.88600 - 11.9269i) q^{15} +(63.6060 + 110.169i) q^{17} +(26.3340 + 78.5208i) q^{19} +(-13.5440 - 23.4589i) q^{21} +(-36.0620 + 62.4612i) q^{23} +(-32.3340 + 56.0042i) q^{25} +53.0000 q^{27} +(-66.3260 + 114.880i) q^{29} -36.6320 q^{31} +(1.84200 + 3.19043i) q^{33} +(186.528 + 323.076i) q^{35} +70.2079 q^{37} -29.1400 q^{39} +(-26.7280 - 46.2943i) q^{41} +(-122.606 - 212.360i) q^{43} -358.072 q^{45} +(19.4460 - 33.6814i) q^{47} +390.760 q^{49} +(-63.6060 + 110.169i) q^{51} +(-276.714 + 479.283i) q^{53} +(-25.3680 - 43.9386i) q^{55} +(-54.8340 + 62.0663i) q^{57} +(-166.872 - 289.031i) q^{59} +(-117.798 + 204.032i) q^{61} +(-352.144 + 609.931i) q^{63} +401.316 q^{65} +(-207.032 + 358.590i) q^{67} -72.1240 q^{69} +(384.342 + 665.700i) q^{71} +(246.468 + 426.895i) q^{73} -64.6680 q^{75} -99.7921 q^{77} +(-16.5340 - 28.6377i) q^{79} +(-324.500 - 562.050i) q^{81} -41.7077 q^{83} +(875.982 - 1517.25i) q^{85} -132.652 q^{87} +(-318.994 + 552.514i) q^{89} +(394.672 - 683.592i) q^{91} +(-18.3160 - 31.7243i) q^{93} +(755.174 - 854.778i) q^{95} +(666.264 + 1154.00i) q^{97} +(47.8919 - 82.9513i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 19 q^{5} - 40 q^{7} + 52 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 - 19 * q^5 - 40 * q^7 + 52 * q^9	$ 4 q + 2 q^{3} - 19 q^{5} - 40 q^{7} + 52 q^{9} + 66 q^{11} - 101 q^{13} + 19 q^{15} + 75 q^{17} - 57 q^{19} - 20 q^{21} + q^{23} + 33 q^{25} + 212 q^{27} + 85 q^{29} - 44 q^{31} + 33 q^{33} + 336 q^{35} + 896 q^{37} - 202 q^{39} - 124 q^{41} - 311 q^{43} - 988 q^{45} + 411 q^{47} + 196 q^{49} - 75 q^{51} - 261 q^{53} - 204 q^{55} - 57 q^{57} + 204 q^{59} - 531 q^{61} - 520 q^{63} + 1554 q^{65} + 556 q^{67} + 2 q^{69} + 1563 q^{71} + 234 q^{73} + 66 q^{75} + 216 q^{77} - 331 q^{79} - 1298 q^{81} - 2918 q^{83} + 1479 q^{85} + 170 q^{87} - 601 q^{89} + 280 q^{91} - 22 q^{93} + 1235 q^{95} + 324 q^{97} + 858 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 19 * q^5 - 40 * q^7 + 52 * q^9 + 66 * q^11 - 101 * q^13 + 19 * q^15 + 75 * q^17 - 57 * q^19 - 20 * q^21 + q^23 + 33 * q^25 + 212 * q^27 + 85 * q^29 - 44 * q^31 + 33 * q^33 + 336 * q^35 + 896 * q^37 - 202 * q^39 - 124 * q^41 - 311 * q^43 - 988 * q^45 + 411 * q^47 + 196 * q^49 - 75 * q^51 - 261 * q^53 - 204 * q^55 - 57 * q^57 + 204 * q^59 - 531 * q^61 - 520 * q^63 + 1554 * q^65 + 556 * q^67 + 2 * q^69 + 1563 * q^71 + 234 * q^73 + 66 * q^75 + 216 * q^77 - 331 * q^79 - 1298 * q^81 - 2918 * q^83 + 1479 * q^85 + 170 * q^87 - 601 * q^89 + 280 * q^91 - 22 * q^93 + 1235 * q^95 + 324 * q^97 + 858 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	0.500000	+	0.866025i	0.0962250	+	0.166667i	0.910119	−	0.414346i	$-0.135990\pi$
$3$	0.500000	+	0.866025i	0.0962250	+	0.166667i	−0.813894	+	0.581013i	$0.802656\pi$
$4$		0			0
$5$	−6.88600	−	11.9269i	−0.615903	−	1.06677i	−0.990225	−	0.139476i	$-0.955458\pi$
$5$	−6.88600	−	11.9269i	−0.615903	−	1.06677i	0.374323	−	0.927298i	$-0.377875\pi$
$6$		0			0
$7$	−27.0880			−1.46261			−0.731307	−	0.682048i	$-0.761090\pi$
$7$	−27.0880			−1.46261			−0.731307	+	0.682048i	$0.761090\pi$
$8$		0			0
$9$	13.0000	−	22.5167i	0.481481	−	0.833950i
$10$		0			0
$11$	3.68399			0.100979			0.0504894	−	0.998725i	$-0.483922\pi$
$11$	3.68399			0.100979			0.0504894	+	0.998725i	$0.483922\pi$
$12$		0			0
$13$	−14.5700	+	25.2360i	−0.310845	+	0.538400i	−0.978546	−	0.206030i	$-0.933945\pi$
$13$	−14.5700	+	25.2360i	−0.310845	+	0.538400i	0.667700	+	0.744430i	$0.267279\pi$
$14$		0			0
$15$	6.88600	−	11.9269i	0.118531	−	0.205301i
$16$		0			0
$17$	63.6060	+	110.169i	0.907454	+	1.57176i	0.817588	+	0.575803i	$0.195311\pi$
$17$	63.6060	+	110.169i	0.907454	+	1.57176i	0.0898663	+	0.995954i	$0.471356\pi$
$18$		0			0
$19$	26.3340	+	78.5208i	0.317970	+	0.948101i
$19$	26.3340	+	78.5208i	0.317970	+	0.948101i
$20$		0			0
$21$	−13.5440	−	23.4589i	−0.140740	−	0.243769i
$22$		0			0
$23$	−36.0620	+	62.4612i	−0.326933	+	0.566264i	−0.981902	−	0.189392i	$-0.939348\pi$
$23$	−36.0620	+	62.4612i	−0.326933	+	0.566264i	0.654969	+	0.755656i	$0.272682\pi$
$24$		0			0
$25$	−32.3340	+	56.0042i	−0.258672	+	0.448033i
$26$		0			0
$27$	53.0000			0.377772
$28$		0			0
$29$	−66.3260	+	114.880i	−0.424705	+	0.735610i	−0.996393	−	0.0848609i	$-0.972955\pi$
$29$	−66.3260	+	114.880i	−0.424705	+	0.735610i	0.571688	+	0.820471i	$0.306289\pi$
$30$		0			0
$31$	−36.6320			−0.212236			−0.106118	−	0.994354i	$-0.533842\pi$
$31$	−36.6320			−0.212236			−0.106118	+	0.994354i	$0.533842\pi$
$32$		0			0
$33$	1.84200	+	3.19043i	0.00971668	+	0.0168298i
$34$		0			0
$35$	186.528	+	323.076i	0.900828	+	1.56028i
$36$		0			0
$37$	70.2079			0.311949			0.155975	−	0.987761i	$-0.450148\pi$
$37$	70.2079			0.311949			0.155975	+	0.987761i	$0.450148\pi$
$38$		0			0
$39$	−29.1400			−0.119644
$40$		0			0
$41$	−26.7280	−	46.2943i	−0.101810	−	0.176340i	0.810620	−	0.585572i	$-0.199130\pi$
$41$	−26.7280	−	46.2943i	−0.101810	−	0.176340i	−0.912430	+	0.409232i	$0.865797\pi$
$42$		0			0
$43$	−122.606	−	212.360i	−0.434820	−	0.753130i	0.562461	−	0.826824i	$-0.309855\pi$
$43$	−122.606	−	212.360i	−0.434820	−	0.753130i	−0.997281	+	0.0736940i	$0.976521\pi$
$44$		0			0
$45$	−358.072			−1.18618
$46$		0			0
$47$	19.4460	−	33.6814i	0.0603508	−	0.104531i	−0.834271	−	0.551354i	$-0.814111\pi$
$47$	19.4460	−	33.6814i	0.0603508	−	0.104531i	0.894622	+	0.446823i	$0.147445\pi$
$48$		0			0
$49$	390.760			1.13924
$50$		0			0
$51$	−63.6060	+	110.169i	−0.174640	+	0.302485i
$52$		0			0
$53$	−276.714	+	479.283i	−0.717162	+	1.24216i	0.244957	+	0.969534i	$0.421226\pi$
$53$	−276.714	+	479.283i	−0.717162	+	1.24216i	−0.962120	+	0.272628i	$0.912107\pi$
$54$		0			0
$55$	−25.3680	−	43.9386i	−0.0621931	−	0.107722i
$56$		0			0
$57$	−54.8340	+	62.0663i	−0.127420	+	0.144226i
$58$		0			0
$59$	−166.872	−	289.031i	−0.368219	−	0.637773i	0.621069	−	0.783756i	$-0.286699\pi$
$59$	−166.872	−	289.031i	−0.368219	−	0.637773i	−0.989287	+	0.145983i	$0.953366\pi$
$60$		0			0
$61$	−117.798	+	204.032i	−0.247254	+	0.428256i	−0.962763	−	0.270347i	$-0.912862\pi$
$61$	−117.798	+	204.032i	−0.247254	+	0.428256i	0.715509	+	0.698604i	$0.246195\pi$
$62$		0			0
$63$	−352.144	+	609.931i	−0.704222	+	1.21975i
$64$		0			0
$65$	401.316			0.765802
$66$		0			0
$67$	−207.032	+	358.590i	−0.377508	+	0.653862i	−0.990699	−	0.136072i	$-0.956552\pi$
$67$	−207.032	+	358.590i	−0.377508	+	0.653862i	0.613191	+	0.789934i	$0.289885\pi$
$68$		0			0
$69$	−72.1240			−0.125836
$70$		0			0
$71$	384.342	+	665.700i	0.642437	+	1.11273i	0.984887	+	0.173197i	$0.0554098\pi$
$71$	384.342	+	665.700i	0.642437	+	1.11273i	−0.342451	+	0.939536i	$0.611257\pi$
$72$		0			0
$73$	246.468	+	426.895i	0.395163	+	0.684443i	0.993122	−	0.117084i	$-0.0373547\pi$
$73$	246.468	+	426.895i	0.395163	+	0.684443i	−0.597959	+	0.801527i	$0.704021\pi$
$74$		0			0
$75$	−64.6680			−0.0995630
$76$		0			0
$77$	−99.7921			−0.147693
$78$		0			0
$79$	−16.5340	−	28.6377i	−0.0235471	−	0.0407847i	0.854012	−	0.520254i	$-0.174163\pi$
$79$	−16.5340	−	28.6377i	−0.0235471	−	0.0407847i	−0.877559	+	0.479469i	$0.840829\pi$
$80$		0			0
$81$	−324.500	−	562.050i	−0.445130	−	0.770988i
$82$		0			0
$83$	−41.7077			−0.0551568			−0.0275784	−	0.999620i	$-0.508780\pi$
$83$	−41.7077			−0.0551568			−0.0275784	+	0.999620i	$0.508780\pi$
$84$		0			0
$85$	875.982	−	1517.25i	1.11781	−	1.93610i
$86$		0			0
$87$	−132.652			−0.163469
$88$		0			0
$89$	−318.994	+	552.514i	−0.379925	+	0.658049i	−0.991051	−	0.133484i	$-0.957383\pi$
$89$	−318.994	+	552.514i	−0.379925	+	0.658049i	0.611126	+	0.791533i	$0.290717\pi$
$90$		0			0
$91$	394.672	−	683.592i	0.454647	−	0.787472i
$92$		0			0
$93$	−18.3160	−	31.7243i	−0.0204224	−	0.0353726i
$94$		0			0
$95$	755.174	−	854.778i	0.815571	−	0.923140i
$96$		0			0
$97$	666.264	+	1154.00i	0.697411	+	1.20795i	0.969361	+	0.245640i	$0.0789982\pi$
$97$	666.264	+	1154.00i	0.697411	+	1.20795i	−0.271950	+	0.962311i	$0.587668\pi$
$98$		0			0
$99$	47.8919	−	82.9513i	0.0486194	−	0.0842113i
$100$		0			0
$101$	175.786	−	304.471i	0.173182	−	0.299960i	−0.766349	−	0.642425i	$-0.777928\pi$
$101$	175.786	−	304.471i	0.173182	−	0.299960i	0.939531	+	0.342465i	$0.111262\pi$
$102$		0			0
$103$	1591.38			1.52237			0.761183	−	0.648537i	$-0.224619\pi$
$103$	1591.38			1.52237			0.761183	+	0.648537i	$0.224619\pi$
$104$		0			0
$105$	−186.528	+	323.076i	−0.173365	+	0.300276i
$106$		0			0
$107$	−974.672			−0.880609			−0.440304	−	0.897849i	$-0.645129\pi$
$107$	−974.672			−0.880609			−0.440304	+	0.897849i	$0.645129\pi$
$108$		0			0
$109$	−643.774	−	1115.05i	−0.565710	−	0.979839i	−0.996983	−	0.0776171i	$-0.975269\pi$
$109$	−643.774	−	1115.05i	−0.565710	−	0.979839i	0.431273	−	0.902221i	$-0.358065\pi$
$110$		0			0
$111$	35.1040	+	60.8019i	0.0300173	+	0.0519915i
$112$		0			0
$113$	−305.484			−0.254315			−0.127157	−	0.991883i	$-0.540585\pi$
$113$	−305.484			−0.254315			−0.127157	+	0.991883i	$0.540585\pi$
$114$		0			0
$115$	993.292			0.805435
$116$		0			0
$117$	378.820	+	656.135i	0.299333	+	0.518459i
$118$		0			0
$119$	−1722.96	−	2984.25i	−1.32726	−	2.29888i
$120$		0			0
$121$	−1317.43			−0.989803
$122$		0			0
$123$	26.7280	−	46.2943i	0.0195934	−	0.0339367i
$124$		0			0
$125$	−830.892			−0.594538
$126$		0			0
$127$	−1298.53	+	2249.11i	−0.907288	+	1.57147i	−0.0894717	+	0.995989i	$0.528518\pi$
$127$	−1298.53	+	2249.11i	−0.907288	+	1.57147i	−0.817816	+	0.575479i	$0.804815\pi$
$128$		0			0
$129$	122.606	−	212.360i	0.0836811	−	0.144940i
$130$		0			0
$131$	−94.1083	−	163.000i	−0.0627655	−	0.108713i	0.832935	−	0.553371i	$-0.186659\pi$
$131$	−94.1083	−	163.000i	−0.0627655	−	0.108713i	−0.895701	+	0.444658i	$0.853325\pi$
$132$		0			0
$133$	−713.336	−	2126.97i	−0.465068	−	1.38671i
$134$		0			0
$135$	−364.958	−	632.126i	−0.232671	−	0.402998i
$136$		0			0
$137$	139.032	−	240.811i	0.0867031	−	0.150174i	−0.819413	−	0.573204i	$-0.805700\pi$
$137$	139.032	−	240.811i	0.0867031	−	0.150174i	0.906116	+	0.423030i	$0.139034\pi$
$138$		0			0
$139$	719.652	−	1246.47i	0.439137	−	0.760608i	−0.558486	−	0.829514i	$-0.688617\pi$
$139$	719.652	−	1246.47i	0.439137	−	0.760608i	0.997623	+	0.0689057i	$0.0219508\pi$
$140$		0			0
$141$	38.8919			0.0232290
$142$		0			0
$143$	−53.6758	+	92.9692i	−0.0313888	+	0.0543669i
$144$		0			0
$145$	1826.88			1.04631
$146$		0			0
$147$	195.380	+	338.408i	0.109624	+	0.189874i
$148$		0			0
$149$	−856.722	−	1483.89i	−0.471043	−	0.815871i	0.528408	−	0.848990i	$-0.322789\pi$
$149$	−856.722	−	1483.89i	−0.471043	−	0.815871i	−0.999451	+	0.0331198i	$0.989456\pi$
$150$		0			0
$151$	−407.640			−0.219690			−0.109845	−	0.993949i	$-0.535036\pi$
$151$	−407.640			−0.219690			−0.109845	+	0.993949i	$0.535036\pi$
$152$		0			0
$153$	3307.51			1.74769
$154$		0			0
$155$	252.248	+	436.906i	0.130716	+	0.226408i
$156$		0			0
$157$	−1232.02	−	2133.93i	−0.626281	−	1.08475i	−0.988292	−	0.152576i	$-0.951243\pi$
$157$	−1232.02	−	2133.93i	−0.626281	−	1.08475i	0.362011	−	0.932174i	$-0.382090\pi$
$158$		0			0
$159$	−553.428			−0.276036
$160$		0			0
$161$	976.848	−	1691.95i	0.478177	−	0.828226i
$162$		0			0
$163$	−142.245			−0.0683526			−0.0341763	−	0.999416i	$-0.510881\pi$
$163$	−142.245			−0.0683526			−0.0341763	+	0.999416i	$0.510881\pi$
$164$		0			0
$165$	25.3680	−	43.9386i	0.0119691	−	0.0207310i
$166$		0			0
$167$	1285.97	−	2227.37i	0.595878	−	1.03209i	−0.397544	−	0.917583i	$-0.630137\pi$
$167$	1285.97	−	2227.37i	0.595878	−	1.03209i	0.993422	−	0.114508i	$-0.0365292\pi$
$168$		0			0
$169$	673.930	+	1167.28i	0.306750	+	0.531307i
$170$		0			0
$171$	2110.37	+	427.817i	0.943766	+	0.191321i
$172$		0			0
$173$	564.094	+	977.039i	0.247903	+	0.429381i	0.962944	−	0.269702i	$-0.0869251\pi$
$173$	564.094	+	977.039i	0.247903	+	0.429381i	−0.715041	+	0.699083i	$0.753592\pi$
$174$		0			0
$175$	875.864	−	1517.04i	0.378338	−	0.655300i
$176$		0			0
$177$	166.872	−	289.031i	0.0708637	−	0.122740i
$178$		0			0
$179$	−4137.46			−1.72764			−0.863822	−	0.503797i	$-0.831936\pi$
$179$	−4137.46			−1.72764			−0.863822	+	0.503797i	$0.831936\pi$
$180$		0			0
$181$	−897.970	+	1555.33i	−0.368760	+	0.638711i	−0.989372	−	0.145407i	$-0.953551\pi$
$181$	−897.970	+	1555.33i	−0.368760	+	0.638711i	0.620612	+	0.784118i	$0.286884\pi$
$182$		0			0
$183$	−235.596			−0.0951681
$184$		0			0
$185$	−483.452	−	837.363i	−0.192130	−	0.332779i
$186$		0			0
$187$	234.324	+	405.861i	0.0916336	+	0.158714i
$188$		0			0
$189$	−1435.66			−0.552536
$190$		0			0
$191$	826.512			0.313111			0.156556	−	0.987669i	$-0.449961\pi$
$191$	826.512			0.313111			0.156556	+	0.987669i	$0.449961\pi$
$192$		0			0
$193$	1990.11	+	3446.97i	0.742235	+	1.28559i	0.951476	+	0.307724i	$0.0995673\pi$
$193$	1990.11	+	3446.97i	0.742235	+	1.28559i	−0.209241	+	0.977864i	$0.567099\pi$
$194$		0			0
$195$	200.658	+	347.550i	0.0736893	+	0.127634i
$196$		0			0
$197$	−186.928			−0.0676046			−0.0338023	−	0.999429i	$-0.510762\pi$
$197$	−186.928			−0.0676046			−0.0338023	+	0.999429i	$0.510762\pi$
$198$		0			0
$199$	−175.662	+	304.255i	−0.0625745	+	0.108382i	−0.895615	−	0.444829i	$-0.853264\pi$
$199$	−175.662	+	304.255i	−0.0625745	+	0.108382i	0.833041	+	0.553211i	$0.186598\pi$
$200$		0			0
$201$	−414.064			−0.145303
$202$		0			0
$203$	1796.64	−	3111.87i	0.621179	−	1.07591i
$204$		0			0
$205$	−368.098	+	637.565i	−0.125410	+	0.217217i
$206$		0			0
$207$	937.612	+	1623.99i	0.314824	+	0.545291i
$208$		0			0
$209$	97.0144	+	289.270i	0.0321083	+	0.0957380i
$210$		0			0
$211$	2373.51	+	4111.05i	0.774405	+	1.34131i	0.935128	+	0.354309i	$0.115284\pi$
$211$	2373.51	+	4111.05i	0.774405	+	1.34131i	−0.160723	+	0.987000i	$0.551383\pi$
$212$		0			0
$213$	−384.342	+	665.700i	−0.123637	+	0.214146i
$214$		0			0
$215$	−1688.53	+	2924.62i	−0.535613	+	0.927709i
$216$		0			0
$217$	992.288			0.310419
$218$		0			0
$219$	−246.468	+	426.895i	−0.0760492	+	0.131721i
$220$		0			0
$221$	−3706.96			−1.12831
$222$		0			0
$223$	644.598	+	1116.48i	0.193567	+	0.335268i	0.946430	−	0.322909i	$-0.104661\pi$
$223$	644.598	+	1116.48i	0.193567	+	0.335268i	−0.752863	+	0.658178i	$0.771328\pi$
$224$		0			0
$225$	840.684	+	1456.11i	0.249092	+	0.431439i
$226$		0			0
$227$	−5742.88			−1.67915			−0.839577	−	0.543240i	$-0.817197\pi$
$227$	−5742.88			−1.67915			−0.839577	+	0.543240i	$0.817197\pi$
$228$		0			0
$229$	−3478.14			−1.00368			−0.501838	−	0.864962i	$-0.667343\pi$
$229$	−3478.14			−1.00368			−0.501838	+	0.864962i	$0.667343\pi$
$230$		0			0
$231$	−49.8960	−	86.4225i	−0.0142118	−	0.0246155i
$232$		0			0
$233$	637.172	+	1103.61i	0.179153	+	0.310301i	0.941591	−	0.336760i	$-0.109331\pi$
$233$	637.172	+	1103.61i	0.179153	+	0.310301i	−0.762438	+	0.647061i	$0.775998\pi$
$234$		0			0
$235$	−535.620			−0.148681
$236$		0			0
$237$	16.5340	−	28.6377i	0.00453163	−	0.00784902i
$238$		0			0
$239$	3154.37			0.853720			0.426860	−	0.904318i	$-0.359620\pi$
$239$	3154.37			0.853720			0.426860	+	0.904318i	$0.359620\pi$
$240$		0			0
$241$	582.303	−	1008.58i	0.155641	−	0.269578i	−0.777651	−	0.628696i	$-0.783589\pi$
$241$	582.303	−	1008.58i	0.155641	−	0.269578i	0.933292	+	0.359118i	$0.116922\pi$
$242$		0			0
$243$	1040.00	−	1801.33i	0.274552	−	0.475537i
$244$		0			0
$245$	−2690.77	−	4660.56i	−0.701662	−	1.21531i
$246$		0			0
$247$	−2365.24	−	479.483i	−0.609297	−	0.123517i
$248$		0			0
$249$	−20.8538	−	36.1199i	−0.00530747	−	0.00919280i
$250$		0			0
$251$	299.592	−	518.908i	0.0753389	−	0.130491i	−0.825895	−	0.563824i	$-0.809329\pi$
$251$	299.592	−	518.908i	0.0753389	−	0.130491i	0.901234	+	0.433334i	$0.142663\pi$
$252$		0			0
$253$	−132.852	+	230.107i	−0.0330132	+	0.0571806i
$254$		0			0
$255$	1751.96			0.430244
$256$		0			0
$257$	−2109.96	+	3654.55i	−0.512122	+	0.887022i	0.487779	+	0.872967i	$0.337807\pi$
$257$	−2109.96	+	3654.55i	−0.512122	+	0.887022i	−0.999901	+	0.0140547i	$0.995526\pi$
$258$		0			0
$259$	−1901.79			−0.456261
$260$		0			0
$261$	1724.48	+	2986.88i	0.408975	+	0.708365i
$262$		0			0
$263$	2719.07	+	4709.57i	0.637511	+	1.10420i	0.985977	+	0.166880i	$0.0533691\pi$
$263$	2719.07	+	4709.57i	0.637511	+	1.10420i	−0.348467	+	0.937321i	$0.613298\pi$
$264$		0			0
$265$	7621.81			1.76681
$266$		0			0
$267$	−637.988			−0.146233
$268$		0			0
$269$	486.330	+	842.348i	0.110231	+	0.190925i	0.915863	−	0.401490i	$-0.131508\pi$
$269$	486.330	+	842.348i	0.110231	+	0.190925i	−0.805633	+	0.592416i	$0.798174\pi$
$270$		0			0
$271$	−1470.31	−	2546.65i	−0.329575	−	0.570841i	0.652852	−	0.757485i	$-0.273572\pi$
$271$	−1470.31	−	2546.65i	−0.329575	−	0.570841i	−0.982428	+	0.186644i	$0.940239\pi$
$272$		0			0
$273$	789.344			0.174994
$274$		0			0
$275$	−119.118	+	206.319i	−0.0261204	+	0.0452418i
$276$		0			0
$277$	−634.968			−0.137731			−0.0688655	−	0.997626i	$-0.521938\pi$
$277$	−634.968			−0.137731			−0.0688655	+	0.997626i	$0.521938\pi$
$278$		0			0
$279$	−476.216	+	824.831i	−0.102188	+	0.176994i
$280$		0			0
$281$	2684.38	−	4649.48i	0.569882	−	0.987064i	−0.426696	−	0.904395i	$-0.640322\pi$
$281$	2684.38	−	4649.48i	0.569882	−	0.987064i	0.996577	−	0.0826685i	$-0.0263443\pi$
$282$		0			0
$283$	8.02851	+	13.9058i	0.00168638	+	0.00292090i	0.866867	−	0.498539i	$-0.166130\pi$
$283$	8.02851	+	13.9058i	0.00168638	+	0.00292090i	−0.865181	+	0.501460i	$0.832797\pi$
$284$		0			0
$285$	1117.85	+	226.611i	0.232335	+	0.0470993i
$286$		0			0
$287$	724.008	+	1254.02i	0.148909	+	0.257918i
$288$		0			0
$289$	−5634.95	+	9760.02i	−1.14695	+	1.98657i
$290$		0			0
$291$	−666.264	+	1154.00i	−0.134217	+	0.232470i
$292$		0			0
$293$	−3611.13			−0.720015			−0.360007	−	0.932949i	$-0.617226\pi$
$293$	−3611.13			−0.720015			−0.360007	+	0.932949i	$0.617226\pi$
$294$		0			0
$295$	−2298.16	+	3980.53i	−0.453574	+	0.785613i
$296$		0			0
$297$	195.252			0.0381470
$298$		0			0
$299$	−1050.85	−	1820.12i	−0.203251	−	0.352041i
$300$		0			0
$301$	3321.15	+	5752.41i	0.635974	+	1.10154i
$302$		0			0
$303$	351.572			0.0666578
$304$		0			0
$305$	3244.63			0.609137
$306$		0			0
$307$	2316.48	+	4012.25i	0.430646	+	0.745901i	0.996929	−	0.0783102i	$-0.0249525\pi$
$307$	2316.48	+	4012.25i	0.430646	+	0.745901i	−0.566283	+	0.824211i	$0.691619\pi$
$308$		0			0
$309$	795.692	+	1378.18i	0.146490	+	0.253728i
$310$		0			0
$311$	−5559.42			−1.01365			−0.506826	−	0.862048i	$-0.669181\pi$
$311$	−5559.42			−1.01365			−0.506826	+	0.862048i	$0.669181\pi$
$312$		0			0
$313$	−3178.29	+	5504.96i	−0.573954	+	0.994117i	0.422201	+	0.906502i	$0.361258\pi$
$313$	−3178.29	+	5504.96i	−0.573954	+	0.994117i	−0.996154	+	0.0876147i	$0.972076\pi$
$314$		0			0
$315$	9699.46			1.73493
$316$		0			0
$317$	3506.82	−	6073.98i	0.621332	−	1.07618i	−0.367905	−	0.929863i	$-0.619925\pi$
$317$	3506.82	−	6073.98i	0.621332	−	1.07618i	0.989238	−	0.146316i	$-0.0467417\pi$
$318$		0			0
$319$	−244.345	+	423.218i	−0.0428861	+	0.0742810i
$320$		0			0
$321$	−487.336	−	844.091i	−0.0847366	−	0.146768i
$322$		0			0
$323$	−6975.55	+	7895.59i	−1.20164	+	1.36013i
$324$		0			0
$325$	−942.213	−	1631.96i	−0.160814	−	0.278538i
$326$		0			0
$327$	643.774	−	1115.05i	0.108871	−	0.188570i
$328$		0			0
$329$	−526.752	+	912.362i	−0.0882699	+	0.152888i
$330$		0			0
$331$	−8531.43			−1.41671			−0.708353	−	0.705858i	$-0.750562\pi$
$331$	−8531.43			−1.41671			−0.708353	+	0.705858i	$0.750562\pi$
$332$		0			0
$333$	912.703	−	1580.85i	0.150198	−	0.260150i
$334$		0			0
$335$	5702.49			0.930031
$336$		0			0
$337$	−3926.57	−	6801.02i	−0.634700	−	1.09933i	−0.986579	−	0.163288i	$-0.947790\pi$
$337$	−3926.57	−	6801.02i	−0.634700	−	1.09933i	0.351878	−	0.936046i	$-0.385543\pi$
$338$		0			0
$339$	−152.742	−	264.557i	−0.0244714	−	0.0423858i
$340$		0			0
$341$	−134.952			−0.0214313
$342$		0			0
$343$	−1293.73			−0.203658
$344$		0			0
$345$	496.646	+	860.216i	0.0775030	+	0.134239i
$346$		0			0
$347$	5273.78	+	9134.46i	0.815884	+	1.41315i	0.908692	+	0.417468i	$0.137082\pi$
$347$	5273.78	+	9134.46i	0.815884	+	1.41315i	−0.0928082	+	0.995684i	$0.529584\pi$
$348$		0			0
$349$	5781.53			0.886757			0.443379	−	0.896334i	$-0.353780\pi$
$349$	5781.53			0.886757			0.443379	+	0.896334i	$0.353780\pi$
$350$		0			0
$351$	−772.210	+	1337.51i	−0.117429	+	0.203393i
$352$		0			0
$353$	−8129.66			−1.22577			−0.612887	−	0.790171i	$-0.709992\pi$
$353$	−8129.66			−1.22577			−0.612887	+	0.790171i	$0.709992\pi$
$354$		0			0
$355$	5293.16	−	9168.02i	0.791357	−	1.37067i
$356$		0			0
$357$	1722.96	−	2984.25i	0.255431	−	0.442419i
$358$		0			0
$359$	−2916.34	−	5051.25i	−0.428742	−	0.742603i	0.568020	−	0.823015i	$-0.307710\pi$
$359$	−2916.34	−	5051.25i	−0.428742	−	0.742603i	−0.996762	+	0.0804118i	$0.974376\pi$
$360$		0			0
$361$	−5472.04	+	4135.54i	−0.797790	+	0.602936i
$362$		0			0
$363$	−658.714	−	1140.93i	−0.0952439	−	0.164967i
$364$		0			0
$365$	3394.36	−	5879.20i	0.486764	−	0.843100i
$366$		0			0
$367$	2972.03	−	5147.70i	0.422721	−	0.732174i	−0.573484	−	0.819217i	$-0.694408\pi$
$367$	2972.03	−	5147.70i	0.422721	−	0.732174i	0.996205	+	0.0870429i	$0.0277417\pi$
$368$		0			0
$369$	−1389.86			−0.196079
$370$		0			0
$371$	7495.63	−	12982.8i	1.04893	−	1.81680i
$372$		0			0
$373$	5999.53			0.832825			0.416413	−	0.909176i	$-0.363287\pi$
$373$	5999.53			0.832825			0.416413	+	0.909176i	$0.363287\pi$
$374$		0			0
$375$	−415.446	−	719.574i	−0.0572094	−	0.0990896i
$376$		0			0
$377$	−1932.74	−	3347.60i	−0.264035	−	0.457322i
$378$		0			0
$379$	8786.72			1.19088			0.595440	−	0.803400i	$-0.296978\pi$
$379$	8786.72			1.19088			0.595440	+	0.803400i	$0.296978\pi$
$380$		0			0
$381$	−2597.05			−0.349215
$382$		0			0
$383$	−5183.88	−	8978.74i	−0.691603	−	1.19789i	−0.971313	−	0.237807i	$-0.923572\pi$
$383$	−5183.88	−	8978.74i	−0.691603	−	1.19789i	0.279710	−	0.960085i	$-0.409762\pi$
$384$		0			0
$385$	687.168	+	1190.21i	0.0909645	+	0.157555i
$386$		0			0
$387$	−6375.51			−0.837430
$388$		0			0
$389$	−2624.21	+	4545.27i	−0.342038	+	0.592428i	−0.984811	−	0.173629i	$-0.944451\pi$
$389$	−2624.21	+	4545.27i	−0.342038	+	0.592428i	0.642773	+	0.766057i	$0.277784\pi$
$390$		0			0
$391$	−9175.05			−1.18671
$392$		0			0
$393$	94.1083	−	163.000i	0.0120792	−	0.0209218i
$394$		0			0
$395$	−227.706	+	394.398i	−0.0290054	+	0.0502388i
$396$		0			0
$397$	−5921.89	−	10257.0i	−0.748643	−	1.29669i	−0.948473	−	0.316857i	$-0.897373\pi$
$397$	−5921.89	−	10257.0i	−0.748643	−	1.29669i	0.199831	−	0.979830i	$-0.435961\pi$
$398$		0			0
$399$	1485.34	−	1681.25i	0.186366	−	0.210947i
$400$		0			0
$401$	−4101.83	−	7104.57i	−0.510812	−	0.884752i	−0.999922	−	0.0125294i	$-0.996012\pi$
$401$	−4101.83	−	7104.57i	−0.510812	−	0.884752i	0.489110	−	0.872222i	$-0.337322\pi$
$402$		0			0
$403$	533.728	−	924.444i	0.0659724	−	0.114268i
$404$		0			0
$405$	−4469.01	+	7740.56i	−0.548314	+	0.949707i
$406$		0			0
$407$	258.646			0.0315002
$408$		0			0
$409$	5596.49	−	9693.40i	0.676598	−	1.17190i	−0.299401	−	0.954127i	$-0.596787\pi$
$409$	5596.49	−	9693.40i	0.676598	−	1.17190i	0.975999	−	0.217775i	$-0.0698798\pi$
$410$		0			0
$411$	278.064			0.0333720
$412$		0			0
$413$	4520.23	+	7829.27i	0.538562	+	0.932817i
$414$		0			0
$415$	287.199	+	497.444i	0.0339712	+	0.0588399i
$416$		0			0
$417$	1439.30			0.169024
$418$		0			0
$419$	−243.522			−0.0283934			−0.0141967	−	0.999899i	$-0.504519\pi$
$419$	−243.522			−0.0283934			−0.0141967	+	0.999899i	$0.504519\pi$
$420$		0			0
$421$	6427.26	+	11132.3i	0.744052	+	1.28874i	0.950637	+	0.310306i	$0.100432\pi$
$421$	6427.26	+	11132.3i	0.744052	+	1.28874i	−0.206585	+	0.978429i	$0.566235\pi$
$422$		0			0
$423$	−505.595	−	875.716i	−0.0581155	−	0.100659i
$424$		0			0
$425$	−8226.55			−0.938933
$426$		0			0
$427$	3190.91	−	5526.82i	0.361637	−	0.626374i
$428$		0			0
$429$	−107.352			−0.0120815
$430$		0			0
$431$	290.227	−	502.688i	0.0324356	−	0.0561801i	−0.849352	−	0.527827i	$-0.823007\pi$
$431$	290.227	−	502.688i	0.0324356	−	0.0561801i	0.881788	+	0.471647i	$0.156340\pi$
$432$		0			0
$433$	4981.09	−	8627.50i	0.552831	−	0.957531i	−0.445238	−	0.895412i	$-0.646881\pi$
$433$	4981.09	−	8627.50i	0.552831	−	0.957531i	0.998069	−	0.0621188i	$-0.0197858\pi$
$434$		0			0
$435$	913.442	+	1582.13i	0.100681	+	0.174384i
$436$		0			0
$437$	−5854.17	−	1186.76i	−0.640830	−	0.129910i
$438$		0			0
$439$	7858.21	+	13610.8i	0.854332	+	1.47975i	0.877263	+	0.480009i	$0.159367\pi$
$439$	7858.21	+	13610.8i	0.854332	+	1.47975i	−0.0229313	+	0.999737i	$0.507300\pi$
$440$		0			0
$441$	5079.88	−	8798.61i	0.548524	−	0.950072i
$442$		0			0
$443$	−3492.82	+	6049.73i	−0.374602	+	0.648830i	−0.990267	−	0.139178i	$-0.955554\pi$
$443$	−3492.82	+	6049.73i	−0.374602	+	0.648830i	0.615665	+	0.788008i	$0.288887\pi$
$444$		0			0
$445$	8786.37			0.935987
$446$		0			0
$447$	856.722	−	1483.89i	0.0906523	−	0.157014i
$448$		0			0
$449$	9815.32			1.03166			0.515828	−	0.856692i	$-0.327484\pi$
$449$	9815.32			1.03166			0.515828	+	0.856692i	$0.327484\pi$
$450$		0			0
$451$	−98.4658	−	170.548i	−0.0102807	−	0.0178066i
$452$		0			0
$453$	−203.820	−	353.026i	−0.0211397	−	0.0366151i
$454$		0			0
$455$	−10870.9			−1.12007
$456$		0			0
$457$	2063.17			0.211183			0.105592	−	0.994410i	$-0.466326\pi$
$457$	2063.17			0.211183			0.105592	+	0.994410i	$0.466326\pi$
$458$		0			0
$459$	3371.12	+	5838.95i	0.342811	+	0.593766i
$460$		0			0
$461$	109.398	+	189.483i	0.0110524	+	0.0191434i	0.871499	−	0.490398i	$-0.163148\pi$
$461$	109.398	+	189.483i	0.0110524	+	0.0191434i	−0.860446	+	0.509541i	$0.829815\pi$
$462$		0			0
$463$	14716.4			1.47717			0.738585	−	0.674160i	$-0.235494\pi$
$463$	14716.4			1.47717			0.738585	+	0.674160i	$0.235494\pi$
$464$		0			0
$465$	−252.248	+	436.906i	−0.0251564	+	0.0435722i
$466$		0			0
$467$	−14620.3			−1.44871			−0.724354	−	0.689428i	$-0.757862\pi$
$467$	−14620.3			−1.44871			−0.724354	+	0.689428i	$0.757862\pi$
$468$		0			0
$469$	5608.09	−	9713.49i	0.552148	−	0.956349i
$470$		0			0
$471$	1232.02	−	2133.93i	0.120528	−	0.208760i
$472$		0			0
$473$	−451.680	−	782.333i	−0.0439075	−	0.0760501i
$474$		0			0
$475$	−5248.98	−	1064.08i	−0.507031	−	0.102786i
$476$		0			0
$477$	7194.57	+	12461.4i	0.690601	+	1.19616i
$478$		0			0
$479$	4162.19	−	7209.13i	0.397026	−	0.687669i	−0.596332	−	0.802738i	$-0.703376\pi$
$479$	4162.19	−	7209.13i	0.397026	−	0.687669i	0.993357	+	0.115069i	$0.0367090\pi$
$480$		0			0
$481$	−1022.93	+	1771.77i	−0.0969679	+	0.167953i
$482$		0			0
$483$	1953.70			0.184050
$484$		0			0
$485$	9175.79	−	15892.9i	0.859075	−	1.48796i
$486$		0			0
$487$	11866.3			1.10413			0.552065	−	0.833801i	$-0.313840\pi$
$487$	11866.3			1.10413			0.552065	+	0.833801i	$0.313840\pi$
$488$		0			0
$489$	−71.1224	−	123.188i	−0.00657724	−	0.0113921i
$490$		0			0
$491$	−5594.08	−	9689.23i	−0.514170	−	0.890568i	−0.999865	−	0.0164397i	$-0.994767\pi$
$491$	−5594.08	−	9689.23i	−0.514170	−	0.890568i	0.485695	−	0.874128i	$-0.338566\pi$
$492$		0			0
$493$	−16874.9			−1.54160
$494$		0			0
$495$	−1319.14			−0.119779
$496$		0			0
$497$	−10411.1	−	18032.5i	−0.939637	−	1.62750i
$498$		0			0
$499$	2361.67	+	4090.53i	0.211870	+	0.366969i	0.952300	−	0.305165i	$-0.0987115\pi$
$499$	2361.67	+	4090.53i	0.211870	+	0.366969i	−0.740430	+	0.672133i	$0.765378\pi$
$500$		0			0
$501$	2571.95			0.229354
$502$		0			0
$503$	−4021.06	+	6964.69i	−0.356442	+	0.617376i	−0.987364	−	0.158471i	$-0.949344\pi$
$503$	−4021.06	+	6964.69i	−0.356442	+	0.617376i	0.630922	+	0.775847i	$0.282677\pi$
$504$		0			0
$505$	−4841.85			−0.426653
$506$		0			0
$507$	−673.930	+	1167.28i	−0.0590341	+	0.102250i
$508$		0			0
$509$	−6664.94	+	11544.0i	−0.580389	+	1.00526i	0.415044	+	0.909801i	$0.363766\pi$
$509$	−6664.94	+	11544.0i	−0.580389	+	1.00526i	−0.995433	+	0.0954622i	$0.969567\pi$
$510$		0			0
$511$	−6676.33	−	11563.7i	−0.577971	−	1.00108i
$512$		0			0
$513$	1395.70	+	4161.60i	0.120120	+	0.358166i
$514$		0			0
$515$	−10958.3	−	18980.3i	−0.937630	−	1.62402i
$516$		0			0
$517$	71.6388	−	124.082i	0.00609414	−	0.0105554i
$518$		0			0
$519$	−564.094	+	977.039i	−0.0477090	+	0.0826344i
$520$		0			0
$521$	−11641.5			−0.978929			−0.489464	−	0.872023i	$-0.662808\pi$
$521$	−11641.5			−0.978929			−0.489464	+	0.872023i	$0.662808\pi$
$522$		0			0
$523$	6306.19	−	10922.6i	0.527247	−	0.913219i	−0.472248	−	0.881466i	$-0.656557\pi$
$523$	6306.19	−	10922.6i	0.527247	−	0.913219i	0.999496	−	0.0317538i	$-0.0101093\pi$
$524$		0			0
$525$	1751.73			0.145622
$526$		0			0
$527$	−2330.02	−	4035.71i	−0.192594	−	0.333583i
$528$		0			0
$529$	3482.56	+	6031.97i	0.286230	+	0.495765i
$530$		0			0
$531$	−8677.35			−0.709162
$532$		0			0
$533$	1557.71			0.126589
$534$		0			0
$535$	6711.59	+	11624.8i	0.542369	+	0.939411i
$536$		0			0
$537$	−2068.73	−	3583.15i	−0.166243	−	0.287941i
$538$		0			0
$539$	1439.56			0.115039
$540$		0			0
$541$	8508.24	−	14736.7i	0.676152	−	1.17113i	−0.299979	−	0.953946i	$-0.596980\pi$
$541$	8508.24	−	14736.7i	0.676152	−	1.17113i	0.976131	−	0.217183i	$-0.0696869\pi$
$542$		0			0
$543$	−1795.94			−0.141936
$544$		0			0
$545$	−8866.06	+	15356.5i	−0.696845	+	1.20697i
$546$		0			0
$547$	140.933	−	244.104i	0.0110162	−	0.0190807i	−0.860465	−	0.509510i	$-0.829827\pi$
$547$	140.933	−	244.104i	0.0110162	−	0.0190807i	0.871481	+	0.490429i	$0.163160\pi$
$548$		0			0
$549$	3062.75	+	5304.83i	0.238096	+	0.412395i
$550$		0			0
$551$	−10767.1	−	2182.72i	−0.832476	−	0.168761i
$552$		0			0
$553$	447.872	+	775.738i	0.0344403	+	0.0596523i
$554$		0			0
$555$	483.452	−	837.363i	0.0369755	−	0.0640434i
$556$		0			0
$557$	−9187.86	+	15913.8i	−0.698926	+	1.21058i	0.269913	+	0.962885i	$0.413005\pi$
$557$	−9187.86	+	15913.8i	−0.698926	+	1.21058i	−0.968839	+	0.247691i	$0.920328\pi$
$558$		0			0
$559$	7145.48			0.540647
$560$		0			0
$561$	−234.324	+	405.861i	−0.0176349	+	0.0305445i
$562$		0			0
$563$	8726.37			0.653238			0.326619	−	0.945156i	$-0.394091\pi$
$563$	8726.37			0.653238			0.326619	+	0.945156i	$0.394091\pi$
$564$		0			0
$565$	2103.57	+	3643.48i	0.156633	+	0.271296i
$566$		0			0
$567$	8790.06	+	15224.8i	0.651054	+	1.12766i
$568$		0			0
$569$	−13771.7			−1.01466			−0.507328	−	0.861753i	$-0.669367\pi$
$569$	−13771.7			−1.01466			−0.507328	+	0.861753i	$0.669367\pi$
$570$		0			0
$571$	25213.4			1.84790			0.923948	−	0.382517i	$-0.124943\pi$
$571$	25213.4			1.84790			0.923948	+	0.382517i	$0.124943\pi$
$572$		0			0
$573$	413.256	+	715.780i	0.0301292	+	0.0521852i
$574$		0			0
$575$	−2332.06	−	4039.25i	−0.169137	−	0.292953i
$576$		0			0
$577$	−8625.99			−0.622365			−0.311182	−	0.950350i	$-0.600725\pi$
$577$	−8625.99			−0.622365			−0.311182	+	0.950350i	$0.600725\pi$
$578$		0			0
$579$	−1990.11	+	3446.97i	−0.142843	+	0.247412i
$580$		0			0
$581$	1129.78			0.0806732
$582$		0			0
$583$	−1019.41	+	1765.68i	−0.0724181	+	0.125432i
$584$		0			0
$585$	5217.11	−	9036.30i	0.368719	−	0.638641i
$586$		0			0
$587$	−1422.17	−	2463.26i	−0.0999985	−	0.173202i	0.811685	−	0.584095i	$-0.198550\pi$
$587$	−1422.17	−	2463.26i	−0.0999985	−	0.173202i	−0.911684	+	0.410893i	$0.865217\pi$
$588$		0			0
$589$	−964.668	−	2876.38i	−0.0674846	−	0.201221i
$590$		0			0
$591$	−93.4642	−	161.885i	−0.00650525	−	0.0112674i
$592$		0			0
$593$	11894.1	−	20601.2i	0.823663	−	1.42663i	−0.0792738	−	0.996853i	$-0.525260\pi$
$593$	11894.1	−	20601.2i	0.823663	−	1.42663i	0.902937	−	0.429773i	$-0.141407\pi$
$594$		0			0
$595$	−23728.6	+	41099.2i	−1.63492	+	2.83177i
$596$		0			0
$597$	−351.323			−0.0240849
$598$		0			0
$599$	−5086.25	+	8809.65i	−0.346943	+	0.600923i	−0.985705	−	0.168482i	$-0.946114\pi$
$599$	−5086.25	+	8809.65i	−0.346943	+	0.600923i	0.638762	+	0.769404i	$0.279447\pi$
$600$		0			0
$601$	4016.48			0.272605			0.136303	−	0.990667i	$-0.456478\pi$
$601$	4016.48			0.272605			0.136303	+	0.990667i	$0.456478\pi$
$602$		0			0
$603$	5382.84	+	9323.35i	0.363526	+	0.629645i
$604$		0			0
$605$	9071.81	+	15712.8i	0.609622	+	1.05590i
$606$		0			0
$607$	8338.65			0.557587			0.278793	−	0.960351i	$-0.410066\pi$
$607$	8338.65			0.557587			0.278793	+	0.960351i	$0.410066\pi$
$608$		0			0
$609$	3593.28			0.239092
$610$		0			0
$611$	566.655	+	981.476i	0.0375195	+	0.0649857i
$612$		0			0
$613$	11257.7	+	19499.0i	0.741754	+	1.28476i	0.951696	+	0.307042i	$0.0993393\pi$
$613$	11257.7	+	19499.0i	0.741754	+	1.28476i	−0.209941	+	0.977714i	$0.567327\pi$
$614$		0			0
$615$	−736.196			−0.0482704
$616$		0			0
$617$	−7338.91	+	12711.4i	−0.478855	+	0.829401i	−0.999706	−	0.0242468i	$-0.992281\pi$
$617$	−7338.91	+	12711.4i	−0.478855	+	0.829401i	0.520851	+	0.853647i	$0.325615\pi$
$618$		0			0
$619$	−22866.5			−1.48478			−0.742392	−	0.669966i	$-0.766309\pi$
$619$	−22866.5			−1.48478			−0.742392	+	0.669966i	$0.766309\pi$
$620$		0			0
$621$	−1911.29	+	3310.45i	−0.123506	+	0.213919i
$622$		0			0
$623$	8640.91	−	14966.5i	0.555684	−	0.962472i
$624$		0			0
$625$	9763.27	+	16910.5i	0.624850	+	1.08227i
$626$		0			0
$627$	−202.008	+	228.652i	−0.0128667	+	0.0145638i
$628$		0			0
$629$	4465.65	+	7734.73i	0.283080	+	0.490308i
$630$		0			0
$631$	−12496.0	+	21643.6i	−0.788362	+	1.36548i	0.138608	+	0.990347i	$0.455737\pi$
$631$	−12496.0	+	21643.6i	−0.788362	+	1.36548i	−0.926970	+	0.375135i	$0.877596\pi$
$632$		0			0
$633$	−2373.51	+	4111.05i	−0.149034	+	0.258135i
$634$		0			0
$635$	35766.6			2.23520
$636$		0			0
$637$	−5693.37	+	9861.21i	−0.354128	+	0.613368i
$638$		0			0
$639$	19985.8			1.23729
$640$		0			0
$641$	−12426.3	−	21522.9i	−0.765692	−	1.32622i	−0.939880	−	0.341505i	$-0.889063\pi$
$641$	−12426.3	−	21522.9i	−0.765692	−	1.32622i	0.174188	−	0.984712i	$-0.444270\pi$
$642$		0			0
$643$	7700.65	+	13337.9i	0.472292	+	0.818034i	0.999497	−	0.0317041i	$-0.0100934\pi$
$643$	7700.65	+	13337.9i	0.472292	+	0.818034i	−0.527205	+	0.849738i	$0.676760\pi$
$644$		0			0
$645$	−3377.06			−0.206158
$646$		0			0
$647$	−18759.3			−1.13989			−0.569943	−	0.821684i	$-0.693035\pi$
$647$	−18759.3			−1.13989			−0.569943	+	0.821684i	$0.693035\pi$
$648$		0			0
$649$	−614.756	−	1064.79i	−0.0371822	−	0.0644015i
$650$		0			0
$651$	496.144	+	859.347i	0.0298701	+	0.0517365i
$652$		0			0
$653$	15027.5			0.900572			0.450286	−	0.892884i	$-0.351322\pi$
$653$	15027.5			0.900572			0.450286	+	0.892884i	$0.351322\pi$
$654$		0			0
$655$	−1296.06	+	2244.84i	−0.0773149	+	0.133913i
$656$		0			0
$657$	12816.3			0.761055
$658$		0			0
$659$	−4258.33	+	7375.64i	−0.251716	+	0.435985i	−0.963998	−	0.265908i	$-0.914328\pi$
$659$	−4258.33	+	7375.64i	−0.251716	+	0.435985i	0.712282	+	0.701893i	$0.247662\pi$
$660$		0			0
$661$	−266.153	+	460.990i	−0.0156613	+	0.0271262i	−0.873750	−	0.486376i	$-0.838319\pi$
$661$	−266.153	+	460.990i	−0.0156613	+	0.0271262i	0.858089	+	0.513502i	$0.171652\pi$
$662$		0			0
$663$	−1853.48	−	3210.32i	−0.108572	−	0.188052i
$664$		0			0
$665$	−20456.2	+	23154.2i	−1.19287	+	1.35020i
$666$		0			0
$667$	−4783.70	−	8285.61i	−0.277700	−	0.480990i
$668$		0			0
$669$	−644.598	+	1116.48i	−0.0372520	+	0.0645224i
$670$		0			0
$671$	−433.967	+	751.653i	−0.0249674	+	0.0432448i
$672$		0			0
$673$	9786.04			0.560511			0.280256	−	0.959925i	$-0.409581\pi$
$673$	9786.04			0.560511			0.280256	+	0.959925i	$0.409581\pi$
$674$		0			0
$675$	−1713.70	+	2968.22i	−0.0977192	+	0.169255i
$676$		0			0
$677$	24769.5			1.40616			0.703079	−	0.711111i	$-0.251808\pi$
$677$	24769.5			1.40616			0.703079	+	0.711111i	$0.251808\pi$
$678$		0			0
$679$	−18047.8	−	31259.7i	−1.02004	−	1.76677i
$680$		0			0
$681$	−2871.44	−	4973.48i	−0.161577	−	0.279859i
$682$		0			0
$683$	−4542.19			−0.254469			−0.127234	−	0.991873i	$-0.540610\pi$
$683$	−4542.19			−0.254469			−0.127234	+	0.991873i	$0.540610\pi$
$684$		0			0
$685$	−3829.50			−0.213603
$686$		0			0
$687$	−1739.07	−	3012.16i	−0.0965788	−	0.167279i
$688$		0			0
$689$	−8063.45	−	13966.3i	−0.445853	−	0.772240i
$690$		0			0
$691$	770.938			0.0424427			0.0212213	−	0.999775i	$-0.493245\pi$
$691$	770.938			0.0424427			0.0212213	+	0.999775i	$0.493245\pi$
$692$		0			0
$693$	−1297.30	+	2246.98i	−0.0711114	+	0.123169i
$694$		0			0
$695$	−19822.1			−1.08186
$696$		0			0
$697$	3400.12	−	5889.19i	0.184776	−	0.320041i
$698$		0			0
$699$	−637.172	+	1103.61i	−0.0344779	+	0.0597175i
$700$		0			0
$701$	−4998.65	−	8657.92i	−0.269325	−	0.466484i	0.699363	−	0.714767i	$-0.253467\pi$
$701$	−4998.65	−	8657.92i	−0.269325	−	0.466484i	−0.968688	+	0.248283i	$0.920134\pi$
$702$		0			0
$703$	1848.86	+	5512.78i	0.0991906	+	0.295759i
$704$		0			0
$705$	−267.810	−	463.860i	−0.0143068	−	0.0247801i
$706$		0			0
$707$	−4761.70	+	8247.50i	−0.253298	+	0.438726i
$708$		0			0
$709$	927.018	−	1605.64i	0.0491042	−	0.0850510i	−0.840429	−	0.541922i	$-0.817697\pi$
$709$	927.018	−	1605.64i	0.0491042	−	0.0850510i	0.889533	+	0.456871i	$0.151030\pi$
$710$		0			0
$711$	−859.766			−0.0453499
$712$		0			0
$713$	1321.02	−	2288.08i	0.0693867	−	0.120181i
$714$		0			0
$715$	1478.45			0.0773297
$716$		0			0
$717$	1577.18	+	2731.76i	0.0821493	+	0.142287i
$718$		0			0
$719$	16730.4	+	28977.9i	0.867786	+	1.50305i	0.864254	+	0.503055i	$0.167791\pi$
$719$	16730.4	+	28977.9i	0.867786	+	1.50305i	0.00353117	+	0.999994i	$0.498876\pi$
$720$		0			0
$721$	−43107.4			−2.22664
$722$		0			0
$723$	1164.61			0.0599062
$724$		0			0
$725$	−4289.17	−	7429.07i	−0.219719	−	0.380564i
$726$		0			0
$727$	−14367.3	−	24884.8i	−0.732947	−	1.26950i	−0.955618	−	0.294607i	$-0.904811\pi$
$727$	−14367.3	−	24884.8i	−0.732947	−	1.26950i	0.222672	−	0.974893i	$-0.428522\pi$
$728$		0			0
$729$	−15443.0			−0.784586
$730$		0			0
$731$	15597.0	−	27014.7i	0.789158	−	1.36686i
$732$		0			0
$733$	11383.3			0.573606			0.286803	−	0.957990i	$-0.407407\pi$
$733$	11383.3			0.573606			0.286803	+	0.957990i	$0.407407\pi$
$734$		0			0
$735$	2690.77	−	4660.56i	0.135035	−	0.233887i
$736$		0			0
$737$	−762.705	+	1321.04i	−0.0381202	+	0.0660262i
$738$		0			0
$739$	−12085.7	−	20933.1i	−0.601598	−	1.04200i	−0.992579	−	0.121600i	$-0.961197\pi$
$739$	−12085.7	−	20933.1i	−0.601598	−	1.04200i	0.390981	−	0.920399i	$-0.372136\pi$
$740$		0			0
$741$	−767.373	−	2288.10i	−0.0380434	−	0.113435i
$742$		0			0
$743$	9127.97	+	15810.1i	0.450704	+	0.780642i	0.998430	−	0.0560160i	$-0.0178398\pi$
$743$	9127.97	+	15810.1i	0.450704	+	0.780642i	−0.547726	+	0.836658i	$0.684506\pi$
$744$		0			0
$745$	−11798.8	+	20436.1i	−0.580233	+	1.00499i
$746$		0			0
$747$	−542.200	+	939.118i	−0.0265570	+	0.0459980i
$748$		0			0
$749$	26401.9			1.28799
$750$		0			0
$751$	−8004.44	+	13864.1i	−0.388930	+	0.673646i	−0.992306	−	0.123811i	$-0.960488\pi$
$751$	−8004.44	+	13864.1i	−0.388930	+	0.673646i	0.603376	+	0.797457i	$0.293822\pi$
$752$		0			0
$753$	599.183			0.0289979
$754$		0			0
$755$	2807.01	+	4861.88i	0.135308	+	0.234360i
$756$		0			0
$757$	17770.8	+	30779.9i	0.853223	+	1.47782i	0.878284	+	0.478139i	$0.158688\pi$
$757$	17770.8	+	30779.9i	0.853223	+	1.47782i	−0.0250617	+	0.999686i	$0.507978\pi$
$758$		0			0
$759$	−265.705			−0.0127068
$760$		0			0
$761$	17849.0			0.850232			0.425116	−	0.905139i	$-0.360233\pi$
$761$	17849.0			0.850232			0.425116	+	0.905139i	$0.360233\pi$
$762$		0			0
$763$	17438.6	+	30204.5i	0.827416	+	1.43313i
$764$		0			0
$765$	−22775.5	−	39448.4i	−1.07641	−	1.86439i
$766$		0			0
$767$	9725.30			0.457836
$768$		0			0
$769$	16150.3	−	27973.2i	0.757341	−	1.31175i	−0.186861	−	0.982386i	$-0.559831\pi$
$769$	16150.3	−	27973.2i	0.757341	−	1.31175i	0.944202	−	0.329367i	$-0.106835\pi$
$770$		0			0
$771$	−4219.91			−0.197116
$772$		0			0
$773$	7996.96	−	13851.1i	0.372097	−	0.644491i	−0.617791	−	0.786342i	$-0.711972\pi$
$773$	7996.96	−	13851.1i	0.372097	−	0.644491i	0.989888	+	0.141852i	$0.0453056\pi$
$774$		0			0
$775$	1184.46	−	2051.55i	0.0548994	−	0.0950886i
$776$		0			0
$777$	−950.897	−	1647.00i	−0.0439038	−	0.0760435i
$778$		0			0
$779$	2931.21	−	3317.82i	0.134816	−	0.152597i
$780$		0			0
$781$	1415.91	+	2452.43i	0.0648724	+	0.112362i
$782$		0			0
$783$	−3515.28	+	6088.64i	−0.160442	+	0.277893i
$784$		0			0
$785$	−16967.4	+	29388.4i	−0.771456	+	1.33620i
$786$		0			0
$787$	−19936.1			−0.902978			−0.451489	−	0.892277i	$-0.649107\pi$
$787$	−19936.1			−0.902978			−0.451489	+	0.892277i	$0.649107\pi$
$788$		0			0
$789$	−2719.07	+	4709.57i	−0.122689	+	0.212504i
$790$		0			0
$791$	8274.96			0.371964
$792$		0			0
$793$	−3432.63	−	5945.49i	−0.153715	−	0.266243i
$794$		0			0
$795$	3810.91	+	6600.68i	0.170011	+	0.294468i
$796$		0			0
$797$	−31005.6			−1.37801			−0.689005	−	0.724756i	$-0.741952\pi$
$797$	−31005.6			−1.37801			−0.689005	+	0.724756i	$0.741952\pi$
$798$		0			0
$799$	4947.52			0.219062
$800$		0			0
$801$	8293.85	+	14365.4i	0.365853	+	0.633677i
$802$		0			0
$803$	907.987	+	1572.68i	0.0399031	+	0.0691141i
$804$		0			0
$805$	−26906.3			−1.17804
$806$		0			0
$807$	−486.330	+	842.348i	−0.0212139	+	0.0367435i
$808$		0			0
$809$	−17553.5			−0.762854			−0.381427	−	0.924399i	$-0.624567\pi$
$809$	−17553.5			−0.762854			−0.381427	+	0.924399i	$0.624567\pi$
$810$		0			0
$811$	15567.9	−	26964.3i	0.674059	−	1.16750i	−0.302684	−	0.953091i	$-0.597883\pi$
$811$	15567.9	−	26964.3i	0.674059	−	1.16750i	0.976743	−	0.214413i	$-0.0687839\pi$
$812$		0			0
$813$	1470.31	−	2546.65i	0.0634268	−	0.109858i
$814$		0			0
$815$	979.498	+	1696.54i	0.0420986	+	0.0729169i
$816$		0			0
$817$	13446.0	−	15219.4i	0.575783	−	0.651726i
$818$		0			0
$819$	−10261.5	−	17773.4i	−0.437808	−	0.758306i
$820$		0			0
$821$	14772.8	−	25587.3i	0.627984	−	1.08770i	−0.359971	−	0.932963i	$-0.617213\pi$
$821$	14772.8	−	25587.3i	0.627984	−	1.08770i	0.987956	−	0.154737i	$-0.0494532\pi$
$822$		0			0
$823$	11823.7	−	20479.2i	0.500786	−	0.867387i	−0.499213	−	0.866479i	$-0.666378\pi$
$823$	11823.7	−	20479.2i	0.500786	−	0.867387i	1.00000		0.000908092i	$-0.000289055\pi$
$824$		0			0
$825$	−238.237			−0.0100537
$826$		0			0
$827$	10204.6	−	17674.9i	0.429079	−	0.743187i	−0.567713	−	0.823227i	$-0.692171\pi$
$827$	10204.6	−	17674.9i	0.429079	−	0.743187i	0.996792	+	0.0800400i	$0.0255048\pi$
$828$		0			0
$829$	−3542.01			−0.148394			−0.0741972	−	0.997244i	$-0.523639\pi$
$829$	−3542.01			−0.148394			−0.0741972	+	0.997244i	$0.523639\pi$
$830$		0			0
$831$	−317.484	−	549.898i	−0.0132532	−	0.0229552i
$832$		0			0
$833$	24854.7	+	43049.6i	1.03381	+	1.79061i
$834$		0			0
$835$	−35420.9			−1.46801
$836$		0			0
$837$	−1941.50			−0.0801767
$838$		0			0
$839$	−219.487	−	380.163i	−0.00903163	−	0.0156432i	0.861474	−	0.507801i	$-0.169542\pi$
$839$	−219.487	−	380.163i	−0.00903163	−	0.0156432i	−0.870506	+	0.492158i	$0.836208\pi$
$840$		0			0
$841$	3396.21	+	5882.41i	0.139252	+	0.241191i
$842$		0			0
$843$	5368.76			0.219348
$844$		0			0
$845$	9281.37	−	16075.8i	0.377857	−	0.654467i
$846$		0			0
$847$	35686.5			1.44770
$848$		0			0
$849$	−8.02851	+	13.9058i	−0.000324544	+	0.000562127i
$850$		0			0
$851$	−2531.84	+	4385.27i	−0.101986	+	0.176645i
$852$		0			0
$853$	−7857.26	−	13609.2i	−0.315390	−	0.546271i	0.664131	−	0.747617i	$-0.268802\pi$
$853$	−7857.26	−	13609.2i	−0.315390	−	0.546271i	−0.979520	+	0.201346i	$0.935469\pi$
$854$		0			0
$855$	−9429.48	−	28116.1i	−0.377171	−	1.12462i
$856$		0			0
$857$	6343.99	+	10988.1i	0.252867	+	0.437978i	0.964314	−	0.264762i	$-0.0852933\pi$
$857$	6343.99	+	10988.1i	0.252867	+	0.437978i	−0.711447	+	0.702739i	$0.751960\pi$
$858$		0			0
$859$	1919.06	−	3323.91i	0.0762253	−	0.132026i	−0.825393	−	0.564558i	$-0.809047\pi$
$859$	1919.06	−	3323.91i	0.0762253	−	0.132026i	0.901618	+	0.432532i	$0.142380\pi$
$860$		0			0
$861$	−724.008	+	1254.02i	−0.0286575	+	0.0496363i
$862$		0			0
$863$	9140.17			0.360527			0.180264	−	0.983618i	$-0.442305\pi$
$863$	9140.17			0.360527			0.180264	+	0.983618i	$0.442305\pi$
$864$		0			0
$865$	7768.70	−	13455.8i	0.305369	−	0.528914i
$866$		0			0
$867$	−11269.9			−0.441460
$868$		0			0
$869$	−60.9111	−	105.501i	−0.00237775	−	0.00411839i
$870$		0			0
$871$	−6032.91	−	10449.3i	−0.234693	−	0.406500i
$872$		0			0
$873$	34645.7			1.34316
$874$		0			0
$875$	22507.2			0.869580
$876$		0			0
$877$	2506.39	+	4341.19i	0.0965049	+	0.167151i	0.910236	−	0.414091i	$-0.135900\pi$
$877$	2506.39	+	4341.19i	0.0965049	+	0.167151i	−0.813731	+	0.581242i	$0.802567\pi$
$878$		0			0
$879$	−1805.56	−	3127.33i	−0.0692835	−	0.120002i
$880$		0			0
$881$	9010.30			0.344568			0.172284	−	0.985047i	$-0.444885\pi$
$881$	9010.30			0.344568			0.172284	+	0.985047i	$0.444885\pi$
$882$		0			0
$883$	7842.63	−	13583.8i	0.298896	−	0.517704i	−0.676987	−	0.735995i	$-0.736715\pi$
$883$	7842.63	−	13583.8i	0.298896	−	0.517704i	0.975884	+	0.218291i	$0.0700481\pi$
$884$		0			0
$885$	−4596.33			−0.174581
$886$		0			0
$887$	138.901	−	240.583i	0.00525798	−	0.00910708i	−0.863384	−	0.504547i	$-0.831660\pi$
$887$	138.901	−	240.583i	0.00525798	−	0.00910708i	0.868642	+	0.495440i	$0.164993\pi$
$888$		0			0
$889$	35174.5	−	60924.0i	1.32701	−	2.29845i
$890$		0			0
$891$	−1195.46	−	2070.59i	−0.0449487	−	0.0778534i
$892$		0			0
$893$	3156.78	+	639.947i	0.118295	+	0.0239810i
$894$		0			0
$895$	28490.6	+	49347.1i	1.06406	+	1.84301i
$896$		0			0
$897$	1050.85	−	1820.12i	0.0391157	−	0.0677503i
$898$		0			0
$899$	2429.66	−	4208.29i	0.0901375	−	0.156123i
$900$		0			0
$901$	−70402.7			−2.60317
$902$		0			0
$903$	−3321.15	+	5752.41i	−0.122393	+	0.211991i
$904$		0			0
$905$	24733.7			0.908481
$906$		0			0
$907$	−21162.2	−	36654.1i	−0.774730	−	1.34187i	−0.934946	−	0.354790i	$-0.884552\pi$
$907$	−21162.2	−	36654.1i	−0.774730	−	1.34187i	0.160216	−	0.987082i	$-0.448781\pi$
$908$		0			0
$909$	−4570.44	−	7916.23i	−0.166768	−	0.288850i
$910$		0			0
$911$	−27419.0			−0.997183			−0.498591	−	0.866837i	$-0.666149\pi$
$911$	−27419.0			−0.997183			−0.498591	+	0.866837i	$0.666149\pi$
$912$		0			0
$913$	−153.651			−0.00556966
$914$		0			0
$915$	1622.31	+	2809.93i	0.0586143	+	0.101523i
$916$		0			0
$917$	2549.21	+	4415.36i	0.0918018	+	0.159005i
$918$		0			0
$919$	−48889.7			−1.75487			−0.877433	−	0.479699i	$-0.840746\pi$
$919$	−48889.7			−1.75487			−0.877433	+	0.479699i	$0.840746\pi$
$920$		0			0
$921$	−2316.48	+	4012.25i	−0.0828778	+	0.143549i
$922$		0			0
$923$	−22399.4			−0.798794
$924$		0			0
$925$	−2270.10	+	3931.94i	−0.0806925	+	0.139764i
$926$		0			0
$927$	20688.0	−	35832.7i	0.732991	−	1.26958i
$928$		0			0
$929$	−25186.1	−	43623.6i	−0.889483	−	1.54063i	−0.840487	−	0.541831i	$-0.817731\pi$
$929$	−25186.1	−	43623.6i	−0.889483	−	1.54063i	−0.0489958	−	0.998799i	$-0.515602\pi$
$930$		0			0
$931$	10290.3	+	30682.8i	0.362245	+	1.08012i
$932$		0			0
$933$	−2779.71	−	4814.60i	−0.0975387	−	0.168942i
$934$		0			0
$935$	3227.11	−	5589.52i	0.112875	−	0.195505i
$936$		0			0
$937$	24039.6	−	41637.8i	0.838142	−	1.45171i	−0.0533035	−	0.998578i	$-0.516975\pi$
$937$	24039.6	−	41637.8i	0.838142	−	1.45171i	0.891446	−	0.453127i	$-0.149692\pi$
$938$		0			0
$939$	−6356.58			−0.220915
$940$		0			0
$941$	15714.1	−	27217.6i	0.544383	−	0.942899i	−0.454263	−	0.890868i	$-0.650097\pi$
$941$	15714.1	−	27217.6i	0.544383	−	0.942899i	0.998645	−	0.0520309i	$-0.0165694\pi$
$942$		0			0
$943$	3855.46			0.133140
$944$		0			0
$945$	9885.99	+	17123.0i	0.340308	+	0.589431i
$946$		0			0
$947$	5500.93	+	9527.88i	0.188760	+	0.326943i	0.944837	−	0.327540i	$-0.106220\pi$
$947$	5500.93	+	9527.88i	0.188760	+	0.326943i	−0.756077	+	0.654483i	$0.772886\pi$
$948$		0			0
$949$	−14364.2			−0.491338
$950$		0			0
$951$	7013.63			0.239151
$952$		0			0
$953$	25157.4	+	43574.0i	0.855120	+	1.48111i	0.876533	+	0.481341i	$0.159850\pi$
$953$	25157.4	+	43574.0i	0.855120	+	1.48111i	−0.0214133	+	0.999771i	$0.506817\pi$
$954$		0			0
$955$	−5691.36	−	9857.72i	−0.192846	−	0.334019i
$956$		0			0
$957$	−488.690			−0.0165069
$958$		0			0
$959$	−3766.10	+	6523.08i	−0.126813	+	0.219647i
$960$		0			0
$961$	−28449.1			−0.954956
$962$		0			0
$963$	−12670.7	+	21946.4i	−0.423997	+	0.734384i
$964$		0			0
$965$	27407.8	−	47471.7i	0.914289	−	1.58359i
$966$		0			0
$967$	−12511.6	−	21670.7i	−0.416077	−	0.720666i	0.579464	−	0.814998i	$-0.303262\pi$
$967$	−12511.6	−	21670.7i	−0.416077	−	0.720666i	−0.995541	+	0.0943319i	$0.969929\pi$
$968$		0			0
$969$	−10325.6	−	2093.21i	−0.342316	−	0.0693948i
$970$		0			0
$971$	4319.90	+	7482.28i	0.142772	+	0.247289i	0.928540	−	0.371233i	$-0.121065\pi$
$971$	4319.90	+	7482.28i	0.142772	+	0.247289i	−0.785767	+	0.618522i	$0.787732\pi$
$972$		0			0
$973$	−19493.9	+	33764.5i	−0.642289	+	1.11248i
$974$		0			0
$975$	942.213	−	1631.96i	0.0309487	−	0.0536047i
$976$		0			0
$977$	4044.17			0.132430			0.0662151	−	0.997805i	$-0.478908\pi$
$977$	4044.17			0.132430			0.0662151	+	0.997805i	$0.478908\pi$
$978$		0			0
$979$	−1175.17	+	2035.46i	−0.0383643	+	0.0664490i
$980$		0			0
$981$	−33476.3			−1.08952
$982$		0			0
$983$	17232.1	+	29846.9i	0.559123	+	0.968430i	0.997570	+	0.0696727i	$0.0221955\pi$
$983$	17232.1	+	29846.9i	0.559123	+	0.968430i	−0.438447	+	0.898757i	$0.644471\pi$
$984$		0			0
$985$	1287.19	+	2229.48i	0.0416378	+	0.0721188i
$986$		0			0
$987$	−1053.50			−0.0339751
$988$		0			0
$989$	17685.7			0.568627
$990$		0			0
$991$	4553.29	+	7886.54i	0.145954	+	0.252799i	0.929728	−	0.368246i	$-0.120042\pi$
$991$	4553.29	+	7886.54i	0.145954	+	0.252799i	−0.783775	+	0.621045i	$0.786708\pi$
$992$		0			0
$993$	−4265.71	−	7388.43i	−0.136323	−	0.236118i
$994$		0			0
$995$	4838.42			0.154159
$996$		0			0
$997$	−28331.7	+	49072.0i	−0.899975	+	1.55880i	−0.0724517	+	0.997372i	$0.523082\pi$
$997$	−28331.7	+	49072.0i	−0.899975	+	1.55880i	−0.827524	+	0.561431i	$0.810251\pi$
$998$		0			0
$999$	3721.02			0.117846

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.4.i.d.273.1		4
4.3	odd	2		19.4.c.b.7.1	✓	4
12.11	even	2		171.4.f.d.64.2		4
19.11	even	3	inner	304.4.i.d.49.1		4
76.7	odd	6		361.4.a.f.1.2		2
76.11	odd	6		19.4.c.b.11.1	yes	4
76.31	even	6		361.4.a.e.1.1		2
228.11	even	6		171.4.f.d.163.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.4.c.b.7.1	✓	4	4.3	odd	2
19.4.c.b.11.1	yes	4	76.11	odd	6
171.4.f.d.64.2		4	12.11	even	2
171.4.f.d.163.2		4	228.11	even	6
304.4.i.d.49.1		4	19.11	even	3	inner
304.4.i.d.273.1		4	1.1	even	1	trivial
361.4.a.e.1.1		2	76.31	even	6
361.4.a.f.1.2		2	76.7	odd	6

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:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	304.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +(-6.88600 - 11.9269i) q^{5} -27.0880 q^{7} +(13.0000 - 22.5167i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{3} +(-6.88600 - 11.9269i) q^{5} -27.0880 q^{7} +(13.0000 - 22.5167i) q^{9} +3.68399 q^{11} +(-14.5700 + 25.2360i) q^{13} +(6.88600 - 11.9269i) q^{15} +(63.6060 + 110.169i) q^{17} +(26.3340 + 78.5208i) q^{19} +(-13.5440 - 23.4589i) q^{21} +(-36.0620 + 62.4612i) q^{23} +(-32.3340 + 56.0042i) q^{25} +53.0000 q^{27} +(-66.3260 + 114.880i) q^{29} -36.6320 q^{31} +(1.84200 + 3.19043i) q^{33} +(186.528 + 323.076i) q^{35} +70.2079 q^{37} -29.1400 q^{39} +(-26.7280 - 46.2943i) q^{41} +(-122.606 - 212.360i) q^{43} -358.072 q^{45} +(19.4460 - 33.6814i) q^{47} +390.760 q^{49} +(-63.6060 + 110.169i) q^{51} +(-276.714 + 479.283i) q^{53} +(-25.3680 - 43.9386i) q^{55} +(-54.8340 + 62.0663i) q^{57} +(-166.872 - 289.031i) q^{59} +(-117.798 + 204.032i) q^{61} +(-352.144 + 609.931i) q^{63} +401.316 q^{65} +(-207.032 + 358.590i) q^{67} -72.1240 q^{69} +(384.342 + 665.700i) q^{71} +(246.468 + 426.895i) q^{73} -64.6680 q^{75} -99.7921 q^{77} +(-16.5340 - 28.6377i) q^{79} +(-324.500 - 562.050i) q^{81} -41.7077 q^{83} +(875.982 - 1517.25i) q^{85} -132.652 q^{87} +(-318.994 + 552.514i) q^{89} +(394.672 - 683.592i) q^{91} +(-18.3160 - 31.7243i) q^{93} +(755.174 - 854.778i) q^{95} +(666.264 + 1154.00i) q^{97} +(47.8919 - 82.9513i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 19 q^{5} - 40 q^{7} + 52 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 - 19 * q^5 - 40 * q^7 + 52 * q^9	\( 4 q + 2 q^{3} - 19 q^{5} - 40 q^{7} + 52 q^{9} + 66 q^{11} - 101 q^{13} + 19 q^{15} + 75 q^{17} - 57 q^{19} - 20 q^{21} + q^{23} + 33 q^{25} + 212 q^{27} + 85 q^{29} - 44 q^{31} + 33 q^{33} + 336 q^{35} + 896 q^{37} - 202 q^{39} - 124 q^{41} - 311 q^{43} - 988 q^{45} + 411 q^{47} + 196 q^{49} - 75 q^{51} - 261 q^{53} - 204 q^{55} - 57 q^{57} + 204 q^{59} - 531 q^{61} - 520 q^{63} + 1554 q^{65} + 556 q^{67} + 2 q^{69} + 1563 q^{71} + 234 q^{73} + 66 q^{75} + 216 q^{77} - 331 q^{79} - 1298 q^{81} - 2918 q^{83} + 1479 q^{85} + 170 q^{87} - 601 q^{89} + 280 q^{91} - 22 q^{93} + 1235 q^{95} + 324 q^{97} + 858 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 19 * q^5 - 40 * q^7 + 52 * q^9 + 66 * q^11 - 101 * q^13 + 19 * q^15 + 75 * q^17 - 57 * q^19 - 20 * q^21 + q^23 + 33 * q^25 + 212 * q^27 + 85 * q^29 - 44 * q^31 + 33 * q^33 + 336 * q^35 + 896 * q^37 - 202 * q^39 - 124 * q^41 - 311 * q^43 - 988 * q^45 + 411 * q^47 + 196 * q^49 - 75 * q^51 - 261 * q^53 - 204 * q^55 - 57 * q^57 + 204 * q^59 - 531 * q^61 - 520 * q^63 + 1554 * q^65 + 556 * q^67 + 2 * q^69 + 1563 * q^71 + 234 * q^73 + 66 * q^75 + 216 * q^77 - 331 * q^79 - 1298 * q^81 - 2918 * q^83 + 1479 * q^85 + 170 * q^87 - 601 * q^89 + 280 * q^91 - 22 * q^93 + 1235 * q^95 + 324 * q^97 + 858 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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