LMFDB - Embedded newform 136.4.k.a.81.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,4,Mod(81,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("136.81");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	136.k (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:	$8.02425976078$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 142x^{12} + 7785x^{10} + 208489x^{8} + 2822686x^{6} + 17977041x^{4} + 45020416x^{2} + 31719424 $ x^14 + 142x^12 + 7785x^10 + 208489x^8 + 2822686x^6 + 17977041x^4 + 45020416x^2 + 31719424
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{17} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			81.5
Root			$-3.07347i$ of defining polynomial
Character	$\chi$	$=$	136.81
Dual form			136.4.k.a.89.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.07347 + 3.07347i) q^{3} +(-8.67626 - 8.67626i) q^{5} +(9.02315 - 9.02315i) q^{7} -8.10760i q^{9} +O(q^{10})$	\(q+(3.07347 + 3.07347i) q^{3} +(-8.67626 - 8.67626i) q^{5} +(9.02315 - 9.02315i) q^{7} -8.10760i q^{9} +(39.0636 - 39.0636i) q^{11} -0.868393 q^{13} -53.3324i q^{15} +(69.8166 + 6.21656i) q^{17} +50.0440i q^{19} +55.4647 q^{21} +(-34.6437 + 34.6437i) q^{23} +25.5549i q^{25} +(107.902 - 107.902i) q^{27} +(100.912 + 100.912i) q^{29} +(-208.341 - 208.341i) q^{31} +240.121 q^{33} -156.574 q^{35} +(-92.7068 - 92.7068i) q^{37} +(-2.66898 - 2.66898i) q^{39} +(127.219 - 127.219i) q^{41} -274.357i q^{43} +(-70.3436 + 70.3436i) q^{45} -92.6014 q^{47} +180.166i q^{49} +(195.473 + 233.685i) q^{51} +460.648i q^{53} -677.851 q^{55} +(-153.808 + 153.808i) q^{57} +539.280i q^{59} +(-456.343 + 456.343i) q^{61} +(-73.1561 - 73.1561i) q^{63} +(7.53440 + 7.53440i) q^{65} -105.099 q^{67} -212.952 q^{69} +(-57.5002 - 57.5002i) q^{71} +(636.819 + 636.819i) q^{73} +(-78.5421 + 78.5421i) q^{75} -704.953i q^{77} +(448.664 - 448.664i) q^{79} +444.362 q^{81} +264.124i q^{83} +(-551.810 - 659.683i) q^{85} +620.297i q^{87} -1573.69 q^{89} +(-7.83564 + 7.83564i) q^{91} -1280.66i q^{93} +(434.194 - 434.194i) q^{95} +(224.583 + 224.583i) q^{97} +(-316.712 - 316.712i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 4 q^{3} + 8 q^{5} - 10 q^{7}+O(q^{10}) $ 14 * q - 4 * q^3 + 8 * q^5 - 10 * q^7	$ 14 q - 4 q^{3} + 8 q^{5} - 10 q^{7} + 16 q^{11} + 72 q^{13} - 40 q^{17} - 60 q^{21} + 246 q^{23} + 572 q^{27} + 260 q^{29} + 566 q^{31} - 904 q^{33} - 804 q^{35} - 28 q^{37} + 476 q^{39} - 786 q^{41} - 604 q^{45} + 448 q^{47} - 380 q^{51} + 1612 q^{55} + 1004 q^{57} + 660 q^{61} - 2250 q^{63} - 796 q^{65} - 284 q^{67} - 2532 q^{69} + 326 q^{71} + 730 q^{73} - 864 q^{75} + 342 q^{79} - 950 q^{81} + 4148 q^{85} - 4516 q^{89} - 3112 q^{91} + 3356 q^{95} - 1194 q^{97} + 2876 q^{99}+O(q^{100}) $ 14 * q - 4 * q^3 + 8 * q^5 - 10 * q^7 + 16 * q^11 + 72 * q^13 - 40 * q^17 - 60 * q^21 + 246 * q^23 + 572 * q^27 + 260 * q^29 + 566 * q^31 - 904 * q^33 - 804 * q^35 - 28 * q^37 + 476 * q^39 - 786 * q^41 - 604 * q^45 + 448 * q^47 - 380 * q^51 + 1612 * q^55 + 1004 * q^57 + 660 * q^61 - 2250 * q^63 - 796 * q^65 - 284 * q^67 - 2532 * q^69 + 326 * q^71 + 730 * q^73 - 864 * q^75 + 342 * q^79 - 950 * q^81 + 4148 * q^85 - 4516 * q^89 - 3112 * q^91 + 3356 * q^95 - 1194 * q^97 + 2876 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	3.07347	+	3.07347i	0.591489	+	0.591489i	0.938034	−	0.346544i	$-0.112645\pi$
$3$	3.07347	+	3.07347i	0.591489	+	0.591489i	−0.346544	+	0.938034i	$0.612645\pi$
$4$		0			0
$5$	−8.67626	−	8.67626i	−0.776028	−	0.776028i	0.203125	−	0.979153i	$-0.434890\pi$
$5$	−8.67626	−	8.67626i	−0.776028	−	0.776028i	−0.979153	+	0.203125i	$0.934890\pi$
$6$		0			0
$7$	9.02315	−	9.02315i	0.487204	−	0.487204i	−0.420219	−	0.907423i	$-0.638047\pi$
$7$	9.02315	−	9.02315i	0.487204	−	0.487204i	0.907423	+	0.420219i	$0.138047\pi$
$8$		0			0
$9$		−	8.10760i		−	0.300281i
$10$		0			0
$11$	39.0636	−	39.0636i	1.07074	−	1.07074i	0.0734374	−	0.997300i	$-0.476603\pi$
$11$	39.0636	−	39.0636i	1.07074	−	1.07074i	0.997300	−	0.0734374i	$-0.0233969\pi$
$12$		0			0
$13$	−0.868393			−0.0185268			−0.00926342	−	0.999957i	$-0.502949\pi$
$13$	−0.868393			−0.0185268			−0.00926342	+	0.999957i	$0.502949\pi$
$14$		0			0
$15$		−	53.3324i		−	0.918024i
$16$		0			0
$17$	69.8166	+	6.21656i	0.996059	+	0.0886904i
$17$	69.8166	+	6.21656i	0.996059	+	0.0886904i
$18$		0			0
$19$			50.0440i			0.604256i	0.953267	+	0.302128i	$0.0976971\pi$
$19$			50.0440i			0.604256i	−0.953267	+	0.302128i	$0.902303\pi$
$20$		0			0
$21$	55.4647			0.576352
$22$		0			0
$23$	−34.6437	+	34.6437i	−0.314074	+	0.314074i	−0.846486	−	0.532412i	$-0.821286\pi$
$23$	−34.6437	+	34.6437i	−0.314074	+	0.314074i	0.532412	+	0.846486i	$0.321286\pi$
$24$		0			0
$25$			25.5549i			0.204439i
$26$		0			0
$27$	107.902	−	107.902i	0.769102	−	0.769102i
$28$		0			0
$29$	100.912	+	100.912i	0.646166	+	0.646166i	0.952064	−	0.305898i	$-0.0989567\pi$
$29$	100.912	+	100.912i	0.646166	+	0.646166i	−0.305898	+	0.952064i	$0.598957\pi$
$30$		0			0
$31$	−208.341	−	208.341i	−1.20707	−	1.20707i	−0.971972	−	0.235095i	$-0.924460\pi$
$31$	−208.341	−	208.341i	−1.20707	−	1.20707i	−0.235095	−	0.971972i	$-0.575540\pi$
$32$		0			0
$33$	240.121			1.26666
$34$		0			0
$35$	−156.574			−0.756168
$36$		0			0
$37$	−92.7068	−	92.7068i	−0.411916	−	0.411916i	0.470489	−	0.882406i	$-0.344077\pi$
$37$	−92.7068	−	92.7068i	−0.411916	−	0.411916i	−0.882406	+	0.470489i	$0.844077\pi$
$38$		0			0
$39$	−2.66898	−	2.66898i	−0.0109584	−	0.0109584i
$40$		0			0
$41$	127.219	−	127.219i	0.484590	−	0.484590i	−0.422004	−	0.906594i	$-0.638673\pi$
$41$	127.219	−	127.219i	0.484590	−	0.484590i	0.906594	+	0.422004i	$0.138673\pi$
$42$		0			0
$43$		−	274.357i		−	0.973001i	−0.873680	−	0.486500i	$-0.838273\pi$
$43$		−	274.357i		−	0.973001i	0.873680	−	0.486500i	$-0.161727\pi$
$44$		0			0
$45$	−70.3436	+	70.3436i	−0.233027	+	0.233027i
$46$		0			0
$47$	−92.6014			−0.287389			−0.143695	−	0.989622i	$-0.545898\pi$
$47$	−92.6014			−0.287389			−0.143695	+	0.989622i	$0.545898\pi$
$48$		0			0
$49$			180.166i			0.525264i
$50$		0			0
$51$	195.473	+	233.685i	0.536699	+	0.641618i
$52$		0			0
$53$			460.648i			1.19386i	0.802292	+	0.596932i	$0.203614\pi$
$53$			460.648i			1.19386i	−0.802292	+	0.596932i	$0.796386\pi$
$54$		0			0
$55$	−677.851			−1.66184
$56$		0			0
$57$	−153.808	+	153.808i	−0.357411	+	0.357411i
$58$		0			0
$59$			539.280i			1.18997i	0.803736	+	0.594986i	$0.202842\pi$
$59$			539.280i			1.18997i	−0.803736	+	0.594986i	$0.797158\pi$
$60$		0			0
$61$	−456.343	+	456.343i	−0.957849	+	0.957849i	−0.999147	−	0.0412984i	$-0.986851\pi$
$61$	−456.343	+	456.343i	−0.957849	+	0.957849i	0.0412984	+	0.999147i	$0.486851\pi$
$62$		0			0
$63$	−73.1561	−	73.1561i	−0.146298	−	0.146298i
$64$		0			0
$65$	7.53440	+	7.53440i	0.0143773	+	0.0143773i
$66$		0			0
$67$	−105.099			−0.191640			−0.0958200	−	0.995399i	$-0.530547\pi$
$67$	−105.099			−0.191640			−0.0958200	+	0.995399i	$0.530547\pi$
$68$		0			0
$69$	−212.952			−0.371543
$70$		0			0
$71$	−57.5002	−	57.5002i	−0.0961129	−	0.0961129i	0.657415	−	0.753528i	$-0.271650\pi$
$71$	−57.5002	−	57.5002i	−0.0961129	−	0.0961129i	−0.753528	+	0.657415i	$0.771650\pi$
$72$		0			0
$73$	636.819	+	636.819i	1.02101	+	1.02101i	0.999774	+	0.0212391i	$0.00676113\pi$
$73$	636.819	+	636.819i	1.02101	+	1.02101i	0.0212391	+	0.999774i	$0.493239\pi$
$74$		0			0
$75$	−78.5421	+	78.5421i	−0.120923	+	0.120923i
$76$		0			0
$77$		−	704.953i		−	1.04334i
$78$		0			0
$79$	448.664	−	448.664i	0.638970	−	0.638970i	−0.311332	−	0.950301i	$-0.600775\pi$
$79$	448.664	−	448.664i	0.638970	−	0.638970i	0.950301	+	0.311332i	$0.100775\pi$
$80$		0			0
$81$	444.362			0.609550
$82$		0			0
$83$			264.124i			0.349293i	0.984631	+	0.174647i	$0.0558783\pi$
$83$			264.124i			0.349293i	−0.984631	+	0.174647i	$0.944122\pi$
$84$		0			0
$85$	−551.810	−	659.683i	−0.704144	−	0.841796i
$86$		0			0
$87$			620.297i			0.764400i
$88$		0			0
$89$	−1573.69			−1.87428			−0.937141	−	0.348951i	$-0.886538\pi$
$89$	−1573.69			−1.87428			−0.937141	+	0.348951i	$0.886538\pi$
$90$		0			0
$91$	−7.83564	+	7.83564i	−0.00902636	+	0.00902636i
$92$		0			0
$93$		−	1280.66i		−	1.42793i
$94$		0			0
$95$	434.194	−	434.194i	0.468920	−	0.468920i
$96$		0			0
$97$	224.583	+	224.583i	0.235082	+	0.235082i	0.814810	−	0.579728i	$-0.196841\pi$
$97$	224.583	+	224.583i	0.235082	+	0.235082i	−0.579728	+	0.814810i	$0.696841\pi$
$98$		0			0
$99$	−316.712	−	316.712i	−0.321522	−	0.321522i
$100$		0			0
$101$	1692.20			1.66713			0.833564	−	0.552423i	$-0.186296\pi$
$101$	1692.20			1.66713			0.833564	+	0.552423i	$0.186296\pi$
$102$		0			0
$103$	642.624			0.614753			0.307377	−	0.951588i	$-0.400549\pi$
$103$	642.624			0.614753			0.307377	+	0.951588i	$0.400549\pi$
$104$		0			0
$105$	−481.226	−	481.226i	−0.447265	−	0.447265i
$106$		0			0
$107$	1188.35	+	1188.35i	1.07366	+	1.07366i	0.997062	+	0.0765994i	$0.0244062\pi$
$107$	1188.35	+	1188.35i	1.07366	+	1.07366i	0.0765994	+	0.997062i	$0.475594\pi$
$108$		0			0
$109$	−526.566	+	526.566i	−0.462714	+	0.462714i	−0.899544	−	0.436830i	$-0.856101\pi$
$109$	−526.566	+	526.566i	−0.462714	+	0.462714i	0.436830	+	0.899544i	$0.356101\pi$
$110$		0			0
$111$		−	569.862i		−	0.487288i
$112$		0			0
$113$	204.185	−	204.185i	0.169983	−	0.169983i	−0.616989	−	0.786972i	$-0.711648\pi$
$113$	204.185	−	204.185i	0.169983	−	0.169983i	0.786972	+	0.616989i	$0.211648\pi$
$114$		0			0
$115$	601.155			0.487460
$116$		0			0
$117$			7.04058i			0.00556327i
$118$		0			0
$119$	686.058	−	573.873i	0.528495	−	0.442074i
$120$		0			0
$121$		−	1720.93i		−	1.29296i
$122$		0			0
$123$	782.004			0.573260
$124$		0			0
$125$	−862.811	+	862.811i	−0.617378	+	0.617378i
$126$		0			0
$127$		−	955.662i		−	0.667726i	−0.942622	−	0.333863i	$-0.891648\pi$
$127$		−	955.662i		−	0.667726i	0.942622	−	0.333863i	$-0.108352\pi$
$128$		0			0
$129$	843.227	−	843.227i	0.575519	−	0.575519i
$130$		0			0
$131$	775.731	+	775.731i	0.517374	+	0.517374i	0.916776	−	0.399402i	$-0.130782\pi$
$131$	775.731	+	775.731i	0.517374	+	0.517374i	−0.399402	+	0.916776i	$0.630782\pi$
$132$		0			0
$133$	451.554	+	451.554i	0.294396	+	0.294396i
$134$		0			0
$135$	−1872.37			−1.19369
$136$		0			0
$137$	−535.781			−0.334123			−0.167061	−	0.985946i	$-0.553428\pi$
$137$	−535.781			−0.334123			−0.167061	+	0.985946i	$0.553428\pi$
$138$		0			0
$139$	555.349	+	555.349i	0.338878	+	0.338878i	0.855945	−	0.517067i	$-0.172976\pi$
$139$	555.349	+	555.349i	0.338878	+	0.338878i	−0.517067	+	0.855945i	$0.672976\pi$
$140$		0			0
$141$	−284.607	−	284.607i	−0.169988	−	0.169988i
$142$		0			0
$143$	−33.9225	+	33.9225i	−0.0198374	+	0.0198374i
$144$		0			0
$145$		−	1751.07i		−	1.00289i
$146$		0			0
$147$	−553.733	+	553.733i	−0.310688	+	0.310688i
$148$		0			0
$149$	2846.15			1.56487			0.782435	−	0.622733i	$-0.213978\pi$
$149$	2846.15			1.56487			0.782435	+	0.622733i	$0.213978\pi$
$150$		0			0
$151$		−	311.072i		−	0.167647i	−0.996481	−	0.0838235i	$-0.973287\pi$
$151$		−	311.072i		−	0.167647i	0.996481	−	0.0838235i	$-0.0267132\pi$
$152$		0			0
$153$	50.4013	−	566.045i	0.0266321	−	0.299098i
$154$		0			0
$155$			3615.24i			1.87344i
$156$		0			0
$157$	−294.137			−0.149521			−0.0747603	−	0.997202i	$-0.523819\pi$
$157$	−294.137			−0.149521			−0.0747603	+	0.997202i	$0.523819\pi$
$158$		0			0
$159$	−1415.79	+	1415.79i	−0.706158	+	0.706158i
$160$		0			0
$161$			625.190i			0.306036i
$162$		0			0
$163$	1717.64	−	1717.64i	0.825372	−	0.825372i	−0.161500	−	0.986873i	$-0.551633\pi$
$163$	1717.64	−	1717.64i	0.825372	−	0.825372i	0.986873	+	0.161500i	$0.0516333\pi$
$164$		0			0
$165$	−2083.35	−	2083.35i	−0.982963	−	0.982963i
$166$		0			0
$167$	−1974.22	−	1974.22i	−0.914790	−	0.914790i	0.0818543	−	0.996644i	$-0.473916\pi$
$167$	−1974.22	−	1974.22i	−0.914790	−	0.914790i	−0.996644	+	0.0818543i	$0.973916\pi$
$168$		0			0
$169$	−2196.25			−0.999657
$170$		0			0
$171$	405.736			0.181447
$172$		0			0
$173$	3015.57	+	3015.57i	1.32526	+	1.32526i	0.909454	+	0.415804i	$0.136500\pi$
$173$	3015.57	+	3015.57i	1.32526	+	1.32526i	0.415804	+	0.909454i	$0.363500\pi$
$174$		0			0
$175$	230.585	+	230.585i	0.0996036	+	0.0996036i
$176$		0			0
$177$	−1657.46	+	1657.46i	−0.703855	+	0.703855i
$178$		0			0
$179$			891.459i			0.372239i	0.982527	+	0.186120i	$0.0595912\pi$
$179$			891.459i			0.372239i	−0.982527	+	0.186120i	$0.940409\pi$
$180$		0			0
$181$	−1545.68	+	1545.68i	−0.634748	+	0.634748i	−0.949255	−	0.314507i	$-0.898161\pi$
$181$	−1545.68	+	1545.68i	−0.634748	+	0.634748i	0.314507	+	0.949255i	$0.398161\pi$
$182$		0			0
$183$	−2805.11			−1.13311
$184$		0			0
$185$			1608.70i			0.639317i
$186$		0			0
$187$	2970.13	−	2484.44i	1.16148	−	0.971554i
$188$		0			0
$189$		−	1947.23i		−	0.749420i
$190$		0			0
$191$	1937.35			0.733937			0.366968	−	0.930233i	$-0.380396\pi$
$191$	1937.35			0.733937			0.366968	+	0.930233i	$0.380396\pi$
$192$		0			0
$193$	−1909.84	+	1909.84i	−0.712298	+	0.712298i	−0.967015	−	0.254718i	$-0.918017\pi$
$193$	−1909.84	+	1909.84i	−0.712298	+	0.712298i	0.254718	+	0.967015i	$0.418017\pi$
$194$		0			0
$195$			46.3135i			0.0170081i
$196$		0			0
$197$	399.215	−	399.215i	0.144380	−	0.144380i	−0.631222	−	0.775602i	$-0.717446\pi$
$197$	399.215	−	399.215i	0.144380	−	0.144380i	0.775602	+	0.631222i	$0.217446\pi$
$198$		0			0
$199$	−3648.28	−	3648.28i	−1.29960	−	1.29960i	−0.928656	−	0.370941i	$-0.879035\pi$
$199$	−3648.28	−	3648.28i	−1.29960	−	1.29960i	−0.370941	−	0.928656i	$-0.620965\pi$
$200$		0			0
$201$	−323.018	−	323.018i	−0.113353	−	0.113353i
$202$		0			0
$203$	1821.08			0.629630
$204$		0			0
$205$	−2207.56			−0.752111
$206$		0			0
$207$	280.877	+	280.877i	0.0943106	+	0.0943106i
$208$		0			0
$209$	1954.90	+	1954.90i	0.647000	+	0.647000i
$210$		0			0
$211$	−3555.86	+	3555.86i	−1.16017	+	1.16017i	−0.175728	+	0.984439i	$0.556228\pi$
$211$	−3555.86	+	3555.86i	−1.16017	+	1.16017i	−0.984439	+	0.175728i	$0.943772\pi$
$212$		0			0
$213$		−	353.450i		−	0.113699i
$214$		0			0
$215$	−2380.39	+	2380.39i	−0.755076	+	0.755076i
$216$		0			0
$217$	−3759.78			−1.17618
$218$		0			0
$219$			3914.48i			1.20784i
$220$		0			0
$221$	−60.6282	−	5.39842i	−0.0184538	−	0.00164315i
$222$		0			0
$223$			485.861i			0.145900i	0.997336	+	0.0729499i	$0.0232413\pi$
$223$			485.861i			0.145900i	−0.997336	+	0.0729499i	$0.976759\pi$
$224$		0			0
$225$	207.189			0.0613892
$226$		0			0
$227$	1690.16	−	1690.16i	0.494183	−	0.494183i	−0.415438	−	0.909621i	$-0.636372\pi$
$227$	1690.16	−	1690.16i	0.494183	−	0.494183i	0.909621	+	0.415438i	$0.136372\pi$
$228$		0			0
$229$		−	187.996i		−	0.0542493i	−0.999632	−	0.0271247i	$-0.991365\pi$
$229$		−	187.996i		−	0.0542493i	0.999632	−	0.0271247i	$-0.00863511\pi$
$230$		0			0
$231$	2166.65	−	2166.65i	0.617122	−	0.617122i
$232$		0			0
$233$	3789.41	+	3789.41i	1.06546	+	1.06546i	0.997702	+	0.0677606i	$0.0215854\pi$
$233$	3789.41	+	3789.41i	1.06546	+	1.06546i	0.0677606	+	0.997702i	$0.478415\pi$
$234$		0			0
$235$	803.433	+	803.433i	0.223022	+	0.223022i
$236$		0			0
$237$	2757.91			0.755887
$238$		0			0
$239$	−4249.16			−1.15002			−0.575011	−	0.818146i	$-0.695002\pi$
$239$	−4249.16			−1.15002			−0.575011	+	0.818146i	$0.695002\pi$
$240$		0			0
$241$	4536.47	+	4536.47i	1.21253	+	1.21253i	0.970192	+	0.242338i	$0.0779143\pi$
$241$	4536.47	+	4536.47i	1.21253	+	1.21253i	0.242338	+	0.970192i	$0.422086\pi$
$242$		0			0
$243$	−1547.62	−	1547.62i	−0.408560	−	0.408560i
$244$		0			0
$245$	1563.16	−	1563.16i	0.407620	−	0.407620i
$246$		0			0
$247$		−	43.4578i		−	0.0111950i
$248$		0			0
$249$	−811.775	+	811.775i	−0.206603	+	0.206603i
$250$		0			0
$251$	529.038			0.133038			0.0665191	−	0.997785i	$-0.478811\pi$
$251$	529.038			0.133038			0.0665191	+	0.997785i	$0.478811\pi$
$252$		0			0
$253$			2706.61i			0.672582i
$254$		0			0
$255$	331.544	−	3723.48i	0.0814199	−	0.914407i
$256$		0			0
$257$		−	4391.33i		−	1.06585i	−0.846162	−	0.532926i	$-0.821093\pi$
$257$		−	4391.33i		−	1.06585i	0.846162	−	0.532926i	$-0.178907\pi$
$258$		0			0
$259$	−1673.01			−0.401375
$260$		0			0
$261$	818.151	−	818.151i	0.194032	−	0.194032i
$262$		0			0
$263$		−	6530.80i		−	1.53120i	−0.643315	−	0.765601i	$-0.722442\pi$
$263$		−	6530.80i		−	1.53120i	0.643315	−	0.765601i	$-0.277558\pi$
$264$		0			0
$265$	3996.70	−	3996.70i	0.926472	−	0.926472i
$266$		0			0
$267$	−4836.69	−	4836.69i	−1.10862	−	1.10862i
$268$		0			0
$269$	5185.75	+	5185.75i	1.17539	+	1.17539i	0.980905	+	0.194488i	$0.0623047\pi$
$269$	5185.75	+	5185.75i	1.17539	+	1.17539i	0.194488	+	0.980905i	$0.437695\pi$
$270$		0			0
$271$	−3156.92			−0.707635			−0.353818	−	0.935314i	$-0.615117\pi$
$271$	−3156.92			−0.707635			−0.353818	+	0.935314i	$0.615117\pi$
$272$		0			0
$273$	−48.1652			−0.0106780
$274$		0			0
$275$	998.265	+	998.265i	0.218900	+	0.218900i
$276$		0			0
$277$	−2386.93	−	2386.93i	−0.517749	−	0.517749i	0.399141	−	0.916890i	$-0.369308\pi$
$277$	−2386.93	−	2386.93i	−0.517749	−	0.517749i	−0.916890	+	0.399141i	$0.869308\pi$
$278$		0			0
$279$	−1689.14	+	1689.14i	−0.362460	+	0.362460i
$280$		0			0
$281$		−	5791.03i		−	1.22941i	−0.788758	−	0.614704i	$-0.789275\pi$
$281$		−	5791.03i		−	1.22941i	0.788758	−	0.614704i	$-0.210725\pi$
$282$		0			0
$283$	5454.87	−	5454.87i	1.14579	−	1.14579i	0.158416	−	0.987372i	$-0.449361\pi$
$283$	5454.87	−	5454.87i	1.14579	−	1.14579i	0.987372	−	0.158416i	$-0.0506386\pi$
$284$		0			0
$285$	2668.96			0.554722
$286$		0			0
$287$		−	2295.82i		−	0.472189i
$288$		0			0
$289$	4835.71	+	868.038i	0.984268	+	0.176682i
$290$		0			0
$291$			1380.50i			0.278097i
$292$		0			0
$293$	−4992.55			−0.995453			−0.497727	−	0.867334i	$-0.665832\pi$
$293$	−4992.55			−0.995453			−0.497727	+	0.867334i	$0.665832\pi$
$294$		0			0
$295$	4678.94	−	4678.94i	0.923451	−	0.923451i
$296$		0			0
$297$		−	8430.08i		−	1.64701i
$298$		0			0
$299$	30.0843	−	30.0843i	0.00581880	−	0.00581880i
$300$		0			0
$301$	−2475.56	−	2475.56i	−0.474050	−	0.474050i
$302$		0			0
$303$	5200.92	+	5200.92i	0.986088	+	0.986088i
$304$		0			0
$305$	7918.70			1.48663
$306$		0			0
$307$	−7425.89			−1.38051			−0.690257	−	0.723564i	$-0.742503\pi$
$307$	−7425.89			−1.38051			−0.690257	+	0.723564i	$0.742503\pi$
$308$		0			0
$309$	1975.08	+	1975.08i	0.363620	+	0.363620i
$310$		0			0
$311$	6145.92	+	6145.92i	1.12059	+	1.12059i	0.991653	+	0.128935i	$0.0411559\pi$
$311$	6145.92	+	6145.92i	1.12059	+	1.12059i	0.128935	+	0.991653i	$0.458844\pi$
$312$		0			0
$313$	−2545.72	+	2545.72i	−0.459720	+	0.459720i	−0.898564	−	0.438843i	$-0.855388\pi$
$313$	−2545.72	+	2545.72i	−0.459720	+	0.459720i	0.438843	+	0.898564i	$0.355388\pi$
$314$		0			0
$315$			1269.44i			0.227063i
$316$		0			0
$317$	−2469.84	+	2469.84i	−0.437603	+	0.437603i	−0.891204	−	0.453602i	$-0.850139\pi$
$317$	−2469.84	+	2469.84i	−0.437603	+	0.437603i	0.453602	+	0.891204i	$0.350139\pi$
$318$		0			0
$319$	7883.94			1.38375
$320$		0			0
$321$			7304.69i			1.27012i
$322$		0			0
$323$	−311.101	+	3493.90i	−0.0535917	+	0.601875i
$324$		0			0
$325$		−	22.1917i		−	0.00378761i
$326$		0			0
$327$	−3236.76			−0.547381
$328$		0			0
$329$	−835.556	+	835.556i	−0.140017	+	0.140017i
$330$		0			0
$331$		−	5092.63i		−	0.845669i	−0.906207	−	0.422834i	$-0.861035\pi$
$331$		−	5092.63i		−	0.845669i	0.906207	−	0.422834i	$-0.138965\pi$
$332$		0			0
$333$	−751.629	+	751.629i	−0.123691	+	0.123691i
$334$		0			0
$335$	911.865	+	911.865i	0.148718	+	0.148718i
$336$		0			0
$337$	−6369.59	−	6369.59i	−1.02960	−	1.02960i	−0.999548	−	0.0300466i	$-0.990434\pi$
$337$	−6369.59	−	6369.59i	−1.02960	−	1.02960i	−0.0300466	−	0.999548i	$-0.509566\pi$
$338$		0			0
$339$	1255.11			0.201086
$340$		0			0
$341$	−16277.1			−2.58490
$342$		0			0
$343$	4720.60	+	4720.60i	0.743115	+	0.743115i
$344$		0			0
$345$	1847.63	+	1847.63i	0.288328	+	0.288328i
$346$		0			0
$347$	−3438.43	+	3438.43i	−0.531943	+	0.531943i	−0.921150	−	0.389207i	$-0.872749\pi$
$347$	−3438.43	+	3438.43i	−0.531943	+	0.531943i	0.389207	+	0.921150i	$0.372749\pi$
$348$		0			0
$349$			2937.29i			0.450514i	0.974299	+	0.225257i	$0.0723221\pi$
$349$			2937.29i			0.450514i	−0.974299	+	0.225257i	$0.927678\pi$
$350$		0			0
$351$	−93.7014	+	93.7014i	−0.0142490	+	0.0142490i
$352$		0			0
$353$	−11318.3			−1.70655			−0.853274	−	0.521462i	$-0.825387\pi$
$353$	−11318.3			−1.70655			−0.853274	+	0.521462i	$0.825387\pi$
$354$		0			0
$355$			997.772i			0.149173i
$356$		0			0
$357$	3872.36	+	344.800i	0.574081	+	0.0511169i
$358$		0			0
$359$			10060.7i			1.47906i	0.673124	+	0.739530i	$0.264952\pi$
$359$			10060.7i			1.47906i	−0.673124	+	0.739530i	$0.735048\pi$
$360$		0			0
$361$	4354.60			0.634874
$362$		0			0
$363$	5289.21	−	5289.21i	0.764770	−	0.764770i
$364$		0			0
$365$		−	11050.4i		−	1.58467i
$366$		0			0
$367$	1489.62	−	1489.62i	0.211873	−	0.211873i	−0.593190	−	0.805063i	$-0.702132\pi$
$367$	1489.62	−	1489.62i	0.211873	−	0.211873i	0.805063	+	0.593190i	$0.202132\pi$
$368$		0			0
$369$	−1031.44	−	1031.44i	−0.145513	−	0.145513i
$370$		0			0
$371$	4156.49	+	4156.49i	0.581656	+	0.581656i
$372$		0			0
$373$	1001.78			0.139062			0.0695312	−	0.997580i	$-0.477850\pi$
$373$	1001.78			0.139062			0.0695312	+	0.997580i	$0.477850\pi$
$374$		0			0
$375$	−5303.65			−0.730344
$376$		0			0
$377$	−87.6310	−	87.6310i	−0.0119714	−	0.0119714i
$378$		0			0
$379$	2198.89	+	2198.89i	0.298020	+	0.298020i	0.840238	−	0.542218i	$-0.182415\pi$
$379$	2198.89	+	2198.89i	0.298020	+	0.298020i	−0.542218	+	0.840238i	$0.682415\pi$
$380$		0			0
$381$	2937.19	−	2937.19i	0.394953	−	0.394953i
$382$		0			0
$383$		−	3039.84i		−	0.405558i	−0.979225	−	0.202779i	$-0.935003\pi$
$383$		−	3039.84i		−	0.405558i	0.979225	−	0.202779i	$-0.0649972\pi$
$384$		0			0
$385$	−6116.35	+	6116.35i	−0.809658	+	0.809658i
$386$		0			0
$387$	−2224.37			−0.292174
$388$		0			0
$389$		−	7047.01i		−	0.918503i	−0.888306	−	0.459252i	$-0.848118\pi$
$389$		−	7047.01i		−	0.918503i	0.888306	−	0.459252i	$-0.151882\pi$
$390$		0			0
$391$	−2634.07	+	2203.34i	−0.340692	+	0.284981i
$392$		0			0
$393$			4768.37i			0.612042i
$394$		0			0
$395$	−7785.44			−0.991717
$396$		0			0
$397$	−2938.84	+	2938.84i	−0.371527	+	0.371527i	−0.868033	−	0.496506i	$-0.834616\pi$
$397$	−2938.84	+	2938.84i	−0.371527	+	0.371527i	0.496506	+	0.868033i	$0.334616\pi$
$398$		0			0
$399$			2775.67i			0.348264i
$400$		0			0
$401$	7877.17	−	7877.17i	0.980965	−	0.980965i	−0.0188573	−	0.999822i	$-0.506003\pi$
$401$	7877.17	−	7877.17i	0.980965	−	0.980965i	0.999822	+	0.0188573i	$0.00600283\pi$
$402$		0			0
$403$	180.922	+	180.922i	0.0223632	+	0.0223632i
$404$		0			0
$405$	−3855.40	−	3855.40i	−0.473028	−	0.473028i
$406$		0			0
$407$	−7242.91			−0.882108
$408$		0			0
$409$	−6227.41			−0.752874			−0.376437	−	0.926442i	$-0.622851\pi$
$409$	−6227.41			−0.752874			−0.376437	+	0.926442i	$0.622851\pi$
$410$		0			0
$411$	−1646.70	−	1646.70i	−0.197630	−	0.197630i
$412$		0			0
$413$	4866.01	+	4866.01i	0.579759	+	0.579759i
$414$		0			0
$415$	2291.60	−	2291.60i	0.271061	−	0.271061i
$416$		0			0
$417$			3413.69i			0.400886i
$418$		0			0
$419$	−1855.27	+	1855.27i	−0.216315	+	0.216315i	−0.806943	−	0.590629i	$-0.798880\pi$
$419$	−1855.27	+	1855.27i	−0.216315	+	0.216315i	0.590629	+	0.806943i	$0.298880\pi$
$420$		0			0
$421$	−13594.4			−1.57376			−0.786878	−	0.617109i	$-0.788304\pi$
$421$	−13594.4			−1.57376			−0.786878	+	0.617109i	$0.788304\pi$
$422$		0			0
$423$			750.774i			0.0862976i
$424$		0			0
$425$	−158.863	+	1784.15i	−0.0181318	+	0.203633i
$426$		0			0
$427$			8235.31i			0.933336i
$428$		0			0
$429$	−208.520			−0.0234672
$430$		0			0
$431$	−5094.94	+	5094.94i	−0.569408	+	0.569408i	−0.931962	−	0.362555i	$-0.881905\pi$
$431$	−5094.94	+	5094.94i	−0.569408	+	0.569408i	0.362555	+	0.931962i	$0.381905\pi$
$432$		0			0
$433$			7430.53i			0.824684i	0.911029	+	0.412342i	$0.135289\pi$
$433$			7430.53i			0.824684i	−0.911029	+	0.412342i	$0.864711\pi$
$434$		0			0
$435$	5381.86	−	5381.86i	0.593196	−	0.593196i
$436$		0			0
$437$	−1733.71	−	1733.71i	−0.189781	−	0.189781i
$438$		0			0
$439$	10536.6	+	10536.6i	1.14553	+	1.14553i	0.987423	+	0.158103i	$0.0505380\pi$
$439$	10536.6	+	10536.6i	1.14553	+	1.14553i	0.158103	+	0.987423i	$0.449462\pi$
$440$		0			0
$441$	1460.71			0.157727
$442$		0			0
$443$	−17733.7			−1.90193			−0.950964	−	0.309302i	$-0.899904\pi$
$443$	−17733.7			−1.90193			−0.950964	+	0.309302i	$0.899904\pi$
$444$		0			0
$445$	13653.8	+	13653.8i	1.45450	+	1.45450i
$446$		0			0
$447$	8747.54	+	8747.54i	0.925603	+	0.925603i
$448$		0			0
$449$	10516.0	−	10516.0i	1.10530	−	1.10530i	0.111544	−	0.993759i	$-0.464420\pi$
$449$	10516.0	−	10516.0i	1.10530	−	1.10530i	0.993759	−	0.111544i	$-0.0355797\pi$
$450$		0			0
$451$		−	9939.22i		−	1.03774i
$452$		0			0
$453$	956.070	−	956.070i	0.0991614	−	0.0991614i
$454$		0			0
$455$	135.968			0.0140094
$456$		0			0
$457$		−	6104.30i		−	0.624829i	−0.949946	−	0.312415i	$-0.898862\pi$
$457$		−	6104.30i		−	0.624829i	0.949946	−	0.312415i	$-0.101138\pi$
$458$		0			0
$459$	8204.13	−	6862.57i	0.834283	−	0.697859i
$460$		0			0
$461$		−	4495.32i		−	0.454160i	−0.973876	−	0.227080i	$-0.927082\pi$
$461$		−	4495.32i		−	0.454160i	0.973876	−	0.227080i	$-0.0729179\pi$
$462$		0			0
$463$	−4964.24			−0.498289			−0.249144	−	0.968466i	$-0.580149\pi$
$463$	−4964.24			−0.498289			−0.249144	+	0.968466i	$0.580149\pi$
$464$		0			0
$465$	−11111.3	+	11111.3i	−1.10812	+	1.10812i
$466$		0			0
$467$		−	789.079i		−	0.0781889i	−0.999236	−	0.0390944i	$-0.987553\pi$
$467$		−	789.079i		−	0.0781889i	0.999236	−	0.0390944i	$-0.0124473\pi$
$468$		0			0
$469$	−948.323	+	948.323i	−0.0933678	+	0.0933678i
$470$		0			0
$471$	−904.022	−	904.022i	−0.0884398	−	0.0884398i
$472$		0			0
$473$	−10717.4	−	10717.4i	−1.04183	−	1.04183i
$474$		0			0
$475$	−1278.87			−0.123534
$476$		0			0
$477$	3734.74			0.358495
$478$		0			0
$479$	2956.32	+	2956.32i	0.281999	+	0.281999i	0.833906	−	0.551907i	$-0.186100\pi$
$479$	2956.32	+	2956.32i	0.281999	+	0.281999i	−0.551907	+	0.833906i	$0.686100\pi$
$480$		0			0
$481$	80.5059	+	80.5059i	0.00763151	+	0.00763151i
$482$		0			0
$483$	−1921.50	+	1921.50i	−0.181017	+	0.181017i
$484$		0			0
$485$		−	3897.08i		−	0.364861i
$486$		0			0
$487$	1159.43	−	1159.43i	0.107883	−	0.107883i	−0.651105	−	0.758988i	$-0.725694\pi$
$487$	1159.43	−	1159.43i	0.107883	−	0.107883i	0.758988	+	0.651105i	$0.225694\pi$
$488$		0			0
$489$	10558.2			0.976398
$490$		0			0
$491$			765.124i			0.0703249i	0.999382	+	0.0351625i	$0.0111949\pi$
$491$			765.124i			0.0703249i	−0.999382	+	0.0351625i	$0.988805\pi$
$492$		0			0
$493$	6417.98	+	7672.63i	0.586311	+	0.700928i
$494$		0			0
$495$			5495.74i			0.499021i
$496$		0			0
$497$	−1037.67			−0.0936532
$498$		0			0
$499$	11036.9	−	11036.9i	0.990142	−	0.990142i	−0.00980984	−	0.999952i	$-0.503123\pi$
$499$	11036.9	−	11036.9i	0.990142	−	0.990142i	0.999952	+	0.00980984i	$0.00312262\pi$
$500$		0			0
$501$		−	12135.4i		−	1.08218i
$502$		0			0
$503$	14656.0	−	14656.0i	1.29917	−	1.29917i	0.370224	−	0.928943i	$-0.379281\pi$
$503$	14656.0	−	14656.0i	1.29917	−	1.29917i	0.928943	−	0.370224i	$-0.120719\pi$
$504$		0			0
$505$	−14681.9	−	14681.9i	−1.29374	−	1.29374i
$506$		0			0
$507$	−6750.09	−	6750.09i	−0.591286	−	0.591286i
$508$		0			0
$509$	20332.9			1.77061			0.885304	−	0.465012i	$-0.153950\pi$
$509$	20332.9			1.77061			0.885304	+	0.465012i	$0.153950\pi$
$510$		0			0
$511$	11492.2			0.994884
$512$		0			0
$513$	5399.85	+	5399.85i	0.464735	+	0.464735i
$514$		0			0
$515$	−5575.57	−	5575.57i	−0.477066	−	0.477066i
$516$		0			0
$517$	−3617.34	+	3617.34i	−0.307718	+	0.307718i
$518$		0			0
$519$			18536.5i			1.56775i
$520$		0			0
$521$	1124.38	−	1124.38i	0.0945490	−	0.0945490i	−0.658250	−	0.752799i	$-0.728703\pi$
$521$	1124.38	−	1124.38i	0.0945490	−	0.0945490i	0.752799	+	0.658250i	$0.228703\pi$
$522$		0			0
$523$	8009.53			0.669660			0.334830	−	0.942278i	$-0.391321\pi$
$523$	8009.53			0.669660			0.334830	+	0.942278i	$0.391321\pi$
$524$		0			0
$525$			1417.39i			0.117829i
$526$		0			0
$527$	−13250.5	−	15840.8i	−1.09526	−	1.30937i
$528$		0			0
$529$			9766.63i			0.802715i
$530$		0			0
$531$	4372.27			0.357326
$532$		0			0
$533$	−110.476	+	110.476i	−0.00897793	+	0.00897793i
$534$		0			0
$535$		−	20620.8i		−	1.66638i
$536$		0			0
$537$	−2739.87	+	2739.87i	−0.220175	+	0.220175i
$538$		0			0
$539$	7037.91	+	7037.91i	0.562420	+	0.562420i
$540$		0			0
$541$	4328.20	+	4328.20i	0.343963	+	0.343963i	0.857855	−	0.513892i	$-0.171797\pi$
$541$	4328.20	+	4328.20i	0.343963	+	0.343963i	−0.513892	+	0.857855i	$0.671797\pi$
$542$		0			0
$543$	−9501.18			−0.750893
$544$		0			0
$545$	9137.24			0.718158
$546$		0			0
$547$	−12109.7	−	12109.7i	−0.946573	−	0.946573i	0.0520704	−	0.998643i	$-0.483418\pi$
$547$	−12109.7	−	12109.7i	−0.946573	−	0.946573i	−0.998643	+	0.0520704i	$0.983418\pi$
$548$		0			0
$549$	3699.85	+	3699.85i	0.287624	+	0.287624i
$550$		0			0
$551$	−5050.02	+	5050.02i	−0.390450	+	0.390450i
$552$		0			0
$553$		−	8096.72i		−	0.622618i
$554$		0			0
$555$	−4944.27	+	4944.27i	−0.378149	+	0.378149i
$556$		0			0
$557$	−1702.39			−0.129502			−0.0647509	−	0.997901i	$-0.520625\pi$
$557$	−1702.39			−0.129502			−0.0647509	+	0.997901i	$0.520625\pi$
$558$		0			0
$559$			238.250i			0.0180266i
$560$		0			0
$561$	16764.4	+	1492.73i	1.26167	+	0.112340i
$562$		0			0
$563$		−	19262.1i		−	1.44192i	−0.692976	−	0.720961i	$-0.743701\pi$
$563$		−	19262.1i		−	1.44192i	0.692976	−	0.720961i	$-0.256299\pi$
$564$		0			0
$565$	−3543.12			−0.263823
$566$		0			0
$567$	4009.54	−	4009.54i	0.296975	−	0.296975i
$568$		0			0
$569$			4320.59i			0.318328i	0.987252	+	0.159164i	$0.0508799\pi$
$569$			4320.59i			0.318328i	−0.987252	+	0.159164i	$0.949120\pi$
$570$		0			0
$571$	−3305.73	+	3305.73i	−0.242277	+	0.242277i	−0.817792	−	0.575514i	$-0.804802\pi$
$571$	−3305.73	+	3305.73i	−0.242277	+	0.242277i	0.575514	+	0.817792i	$0.304802\pi$
$572$		0			0
$573$	5954.39	+	5954.39i	0.434116	+	0.434116i
$574$		0			0
$575$	−885.314	−	885.314i	−0.0642090	−	0.0642090i
$576$		0			0
$577$	−4858.52			−0.350542			−0.175271	−	0.984520i	$-0.556080\pi$
$577$	−4858.52			−0.350542			−0.175271	+	0.984520i	$0.556080\pi$
$578$		0			0
$579$	−11739.7			−0.842633
$580$		0			0
$581$	2383.23	+	2383.23i	0.170177	+	0.170177i
$582$		0			0
$583$	17994.5	+	17994.5i	1.27832	+	1.27832i
$584$		0			0
$585$	61.0859	−	61.0859i	0.00431725	−	0.00431725i
$586$		0			0
$587$		−	27354.2i		−	1.92339i	−0.274125	−	0.961694i	$-0.588388\pi$
$587$		−	27354.2i		−	1.92339i	0.274125	−	0.961694i	$-0.411612\pi$
$588$		0			0
$589$	10426.2	−	10426.2i	0.729378	−	0.729378i
$590$		0			0
$591$	2453.95			0.170799
$592$		0			0
$593$			13606.3i			0.942233i	0.882071	+	0.471117i	$0.156149\pi$
$593$			13606.3i			0.942233i	−0.882071	+	0.471117i	$0.843851\pi$
$594$		0			0
$595$	−10931.5	−	973.353i	−0.753189	−	0.0670649i
$596$		0			0
$597$		−	22425.8i		−	1.53740i
$598$		0			0
$599$	17513.3			1.19461			0.597307	−	0.802013i	$-0.296238\pi$
$599$	17513.3			1.19461			0.597307	+	0.802013i	$0.296238\pi$
$600$		0			0
$601$	−13737.7	+	13737.7i	−0.932399	+	0.932399i	−0.997855	−	0.0654564i	$-0.979150\pi$
$601$	−13737.7	+	13737.7i	−0.932399	+	0.932399i	0.0654564	+	0.997855i	$0.479150\pi$
$602$		0			0
$603$			852.099i			0.0575459i
$604$		0			0
$605$	−14931.2	+	14931.2i	−1.00337	+	1.00337i
$606$		0			0
$607$	4673.11	+	4673.11i	0.312480	+	0.312480i	0.845870	−	0.533389i	$-0.179082\pi$
$607$	4673.11	+	4673.11i	0.312480	+	0.312480i	−0.533389	+	0.845870i	$0.679082\pi$
$608$		0			0
$609$	5597.03	+	5597.03i	0.372419	+	0.372419i
$610$		0			0
$611$	80.4144			0.00532442
$612$		0			0
$613$	24289.4			1.60039			0.800196	−	0.599739i	$-0.204729\pi$
$613$	24289.4			1.60039			0.800196	+	0.599739i	$0.204729\pi$
$614$		0			0
$615$	−6784.87	−	6784.87i	−0.444866	−	0.444866i
$616$		0			0
$617$	−19700.6	−	19700.6i	−1.28544	−	1.28544i	−0.937526	−	0.347915i	$-0.886890\pi$
$617$	−19700.6	−	19700.6i	−1.28544	−	1.28544i	−0.347915	−	0.937526i	$-0.613110\pi$
$618$		0			0
$619$	−21044.4	+	21044.4i	−1.36647	+	1.36647i	−0.501055	+	0.865415i	$0.667055\pi$
$619$	−21044.4	+	21044.4i	−1.36647	+	1.36647i	−0.865415	+	0.501055i	$0.832945\pi$
$620$		0			0
$621$			7476.24i			0.483110i
$622$		0			0
$623$	−14199.7	+	14199.7i	−0.913158	+	0.913158i
$624$		0			0
$625$	18166.3			1.16264
$626$		0			0
$627$			12016.6i			0.765387i
$628$		0			0
$629$	−5896.15	−	7048.79i	−0.373760	−	0.446826i
$630$		0			0
$631$			3117.99i			0.196712i	0.995151	+	0.0983559i	$0.0313584\pi$
$631$			3117.99i			0.196712i	−0.995151	+	0.0983559i	$0.968642\pi$
$632$		0			0
$633$	−21857.6			−1.37245
$634$		0			0
$635$	−8291.56	+	8291.56i	−0.518174	+	0.518174i
$636$		0			0
$637$		−	156.455i		−	0.00973148i
$638$		0			0
$639$	−466.188	+	466.188i	−0.0288609	+	0.0288609i
$640$		0			0
$641$	−1391.32	−	1391.32i	−0.0857314	−	0.0857314i	0.662941	−	0.748672i	$-0.269308\pi$
$641$	−1391.32	−	1391.32i	−0.0857314	−	0.0857314i	−0.748672	+	0.662941i	$0.769308\pi$
$642$		0			0
$643$	3638.34	+	3638.34i	0.223145	+	0.223145i	0.809821	−	0.586676i	$-0.199564\pi$
$643$	3638.34	+	3638.34i	0.223145	+	0.223145i	−0.586676	+	0.809821i	$0.699564\pi$
$644$		0			0
$645$	−14632.1			−0.893238
$646$		0			0
$647$	−3564.67			−0.216602			−0.108301	−	0.994118i	$-0.534541\pi$
$647$	−3564.67			−0.216602			−0.108301	+	0.994118i	$0.534541\pi$
$648$		0			0
$649$	21066.2	+	21066.2i	1.27415	+	1.27415i
$650$		0			0
$651$	−11555.6	−	11555.6i	−0.695696	−	0.695696i
$652$		0			0
$653$	−19594.4	+	19594.4i	−1.17425	+	1.17425i	−0.193070	+	0.981185i	$0.561844\pi$
$653$	−19594.4	+	19594.4i	−1.17425	+	1.17425i	−0.981185	+	0.193070i	$0.938156\pi$
$654$		0			0
$655$		−	13460.9i		−	0.802993i
$656$		0			0
$657$	5163.07	−	5163.07i	0.306591	−	0.306591i
$658$		0			0
$659$	3093.29			0.182849			0.0914245	−	0.995812i	$-0.470858\pi$
$659$	3093.29			0.182849			0.0914245	+	0.995812i	$0.470858\pi$
$660$		0			0
$661$			26602.2i			1.56537i	0.622420	+	0.782683i	$0.286149\pi$
$661$			26602.2i			1.56537i	−0.622420	+	0.782683i	$0.713851\pi$
$662$		0			0
$663$	−169.747	−	202.931i	−0.00994333	−	0.0118871i
$664$		0			0
$665$		−	7835.60i		−	0.456920i
$666$		0			0
$667$	−6991.90			−0.405888
$668$		0			0
$669$	−1493.28	+	1493.28i	−0.0862981	+	0.0862981i
$670$		0			0
$671$			35652.8i			2.05121i
$672$		0			0
$673$	−11937.4	+	11937.4i	−0.683736	+	0.683736i	−0.960840	−	0.277104i	$-0.910625\pi$
$673$	−11937.4	+	11937.4i	−0.683736	+	0.683736i	0.277104	+	0.960840i	$0.410625\pi$
$674$		0			0
$675$	2757.42	+	2757.42i	0.157234	+	0.157234i
$676$		0			0
$677$	2726.21	+	2726.21i	0.154766	+	0.154766i	0.780243	−	0.625477i	$-0.215095\pi$
$677$	2726.21	+	2726.21i	0.154766	+	0.154766i	−0.625477	+	0.780243i	$0.715095\pi$
$678$		0			0
$679$	4052.89			0.229066
$680$		0			0
$681$	10389.3			0.584608
$682$		0			0
$683$	−16602.4	−	16602.4i	−0.930123	−	0.930123i	0.0675904	−	0.997713i	$-0.478469\pi$
$683$	−16602.4	−	16602.4i	−0.930123	−	0.930123i	−0.997713	+	0.0675904i	$0.978469\pi$
$684$		0			0
$685$	4648.57	+	4648.57i	0.259289	+	0.259289i
$686$		0			0
$687$	577.798	−	577.798i	0.0320879	−	0.0320879i
$688$		0			0
$689$		−	400.023i		−	0.0221185i
$690$		0			0
$691$	10570.1	−	10570.1i	0.581920	−	0.581920i	−0.353511	−	0.935431i	$-0.615012\pi$
$691$	10570.1	−	10570.1i	0.581920	−	0.581920i	0.935431	+	0.353511i	$0.115012\pi$
$692$		0			0
$693$	−5715.47			−0.313294
$694$		0			0
$695$		−	9636.70i		−	0.525958i
$696$		0			0
$697$	9672.83	−	8091.10i	0.525659	−	0.439702i
$698$		0			0
$699$			23293.3i			1.26042i
$700$		0			0
$701$	−8204.92			−0.442076			−0.221038	−	0.975265i	$-0.570945\pi$
$701$	−8204.92			−0.442076			−0.221038	+	0.975265i	$0.570945\pi$
$702$		0			0
$703$	4639.41	−	4639.41i	0.248903	−	0.248903i
$704$		0			0
$705$			4938.65i			0.263830i
$706$		0			0
$707$	15269.0	−	15269.0i	0.812232	−	0.812232i
$708$		0			0
$709$	−15750.5	−	15750.5i	−0.834304	−	0.834304i	0.153798	−	0.988102i	$-0.450849\pi$
$709$	−15750.5	−	15750.5i	−0.834304	−	0.834304i	−0.988102	+	0.153798i	$0.950849\pi$
$710$		0			0
$711$	−3637.58	−	3637.58i	−0.191871	−	0.191871i
$712$		0			0
$713$	14435.4			0.758217
$714$		0			0
$715$	588.641			0.0307887
$716$		0			0
$717$	−13059.6	−	13059.6i	−0.680225	−	0.680225i
$718$		0			0
$719$	−10899.1	−	10899.1i	−0.565326	−	0.565326i	0.365489	−	0.930816i	$-0.380902\pi$
$719$	−10899.1	−	10899.1i	−0.565326	−	0.565326i	−0.930816	+	0.365489i	$0.880902\pi$
$720$		0			0
$721$	5798.49	−	5798.49i	0.299511	−	0.299511i
$722$		0			0
$723$			27885.4i			1.43440i
$724$		0			0
$725$	−2578.78	+	2578.78i	−0.132102	+	0.132102i
$726$		0			0
$727$	−597.129			−0.0304626			−0.0152313	−	0.999884i	$-0.504848\pi$
$727$	−597.129			−0.0304626			−0.0152313	+	0.999884i	$0.504848\pi$
$728$		0			0
$729$		−	21510.9i		−	1.09287i
$730$		0			0
$731$	1705.56	−	19154.7i	0.0862958	−	0.969166i
$732$		0			0
$733$		−	16993.0i		−	0.856274i	−0.903714	−	0.428137i	$-0.859170\pi$
$733$		−	16993.0i		−	0.856274i	0.903714	−	0.428137i	$-0.140830\pi$
$734$		0			0
$735$	9608.66			0.482205
$736$		0			0
$737$	−4105.54	+	4105.54i	−0.205196	+	0.205196i
$738$		0			0
$739$			37983.6i			1.89073i	0.326017	+	0.945364i	$0.394293\pi$
$739$			37983.6i			1.89073i	−0.326017	+	0.945364i	$0.605707\pi$
$740$		0			0
$741$	133.566	−	133.566i	0.00662170	−	0.00662170i
$742$		0			0
$743$	2340.76	+	2340.76i	0.115578	+	0.115578i	0.762530	−	0.646953i	$-0.223957\pi$
$743$	2340.76	+	2340.76i	0.115578	+	0.115578i	−0.646953	+	0.762530i	$0.723957\pi$
$744$		0			0
$745$	−24693.9	−	24693.9i	−1.21438	−	1.21438i
$746$		0			0
$747$	2141.41			0.104886
$748$		0			0
$749$	21445.3			1.04618
$750$		0			0
$751$	−13570.6	−	13570.6i	−0.659383	−	0.659383i	0.295851	−	0.955234i	$-0.404397\pi$
$751$	−13570.6	−	13570.6i	−0.659383	−	0.659383i	−0.955234	+	0.295851i	$0.904397\pi$
$752$		0			0
$753$	1625.98	+	1625.98i	0.0786907	+	0.0786907i
$754$		0			0
$755$	−2698.94	+	2698.94i	−0.130099	+	0.130099i
$756$		0			0
$757$		−	2949.36i		−	0.141607i	−0.997490	−	0.0708035i	$-0.977444\pi$
$757$		−	2949.36i		−	0.141607i	0.997490	−	0.0708035i	$-0.0225563\pi$
$758$		0			0
$759$	−8318.68	+	8318.68i	−0.397825	+	0.397825i
$760$		0			0
$761$	−21295.1			−1.01438			−0.507192	−	0.861833i	$-0.669317\pi$
$761$	−21295.1			−1.01438			−0.507192	+	0.861833i	$0.669317\pi$
$762$		0			0
$763$			9502.56i			0.450873i
$764$		0			0
$765$	−5348.44	+	4473.85i	−0.252776	+	0.211441i
$766$		0			0
$767$		−	468.308i		−	0.0220464i
$768$		0			0
$769$	27668.1			1.29745			0.648724	−	0.761024i	$-0.275303\pi$
$769$	27668.1			1.29745			0.648724	+	0.761024i	$0.275303\pi$
$770$		0			0
$771$	13496.6	−	13496.6i	0.630439	−	0.630439i
$772$		0			0
$773$		−	19775.2i		−	0.920133i	−0.887884	−	0.460067i	$-0.847826\pi$
$773$		−	19775.2i		−	0.920133i	0.887884	−	0.460067i	$-0.152174\pi$
$774$		0			0
$775$	5324.12	−	5324.12i	0.246772	−	0.246772i
$776$		0			0
$777$	−5141.95	−	5141.95i	−0.237409	−	0.237409i
$778$		0			0
$779$	6366.52	+	6366.52i	0.292817	+	0.292817i
$780$		0			0
$781$	−4492.32			−0.205823
$782$		0			0
$783$	21777.1			0.993936
$784$		0			0
$785$	2552.01	+	2552.01i	0.116032	+	0.116032i
$786$		0			0
$787$	−3947.52	−	3947.52i	−0.178798	−	0.178798i	0.612034	−	0.790832i	$-0.290352\pi$
$787$	−3947.52	−	3947.52i	−0.178798	−	0.178798i	−0.790832	+	0.612034i	$0.790352\pi$
$788$		0			0
$789$	20072.2	−	20072.2i	0.905690	−	0.905690i
$790$		0			0
$791$		−	3684.78i		−	0.165633i
$792$		0			0
$793$	396.285	−	396.285i	0.0177459	−	0.0177459i
$794$		0			0
$795$	24567.4			1.09600
$796$		0			0
$797$			16897.8i			0.751006i	0.926821	+	0.375503i	$0.122530\pi$
$797$			16897.8i			0.751006i	−0.926821	+	0.375503i	$0.877470\pi$
$798$		0			0
$799$	−6465.11	−	575.662i	−0.286257	−	0.0254887i
$800$		0			0
$801$			12758.9i			0.562812i
$802$		0			0
$803$	49752.8			2.18647
$804$		0			0
$805$	5424.31	−	5424.31i	0.237493	−	0.237493i
$806$		0			0
$807$			31876.5i			1.39046i
$808$		0			0
$809$	−21479.4	+	21479.4i	−0.933467	+	0.933467i	−0.997921	−	0.0644539i	$-0.979469\pi$
$809$	−21479.4	+	21479.4i	−0.933467	+	0.933467i	0.0644539	+	0.997921i	$0.479469\pi$
$810$		0			0
$811$	29914.5	+	29914.5i	1.29524	+	1.29524i	0.931501	+	0.363740i	$0.118500\pi$
$811$	29914.5	+	29914.5i	1.29524	+	1.29524i	0.363740	+	0.931501i	$0.381500\pi$
$812$		0			0
$813$	−9702.69	−	9702.69i	−0.418559	−	0.418559i
$814$		0			0
$815$	−29805.3			−1.28102
$816$		0			0
$817$	13729.9			0.587942
$818$		0			0
$819$	63.5282	+	63.5282i	0.00271045	+	0.00271045i
$820$		0			0
$821$	−9116.42	−	9116.42i	−0.387534	−	0.387534i	0.486273	−	0.873807i	$-0.338356\pi$
$821$	−9116.42	−	9116.42i	−0.387534	−	0.387534i	−0.873807	+	0.486273i	$0.838356\pi$
$822$		0			0
$823$	26462.2	−	26462.2i	1.12079	−	1.12079i	0.129171	−	0.991622i	$-0.458768\pi$
$823$	26462.2	−	26462.2i	1.12079	−	1.12079i	0.991622	−	0.129171i	$-0.0412316\pi$
$824$		0			0
$825$			6136.27i			0.258954i
$826$		0			0
$827$	9620.86	−	9620.86i	0.404535	−	0.404535i	−0.475293	−	0.879828i	$-0.657658\pi$
$827$	9620.86	−	9620.86i	0.404535	−	0.404535i	0.879828	+	0.475293i	$0.157658\pi$
$828$		0			0
$829$	−14740.5			−0.617562			−0.308781	−	0.951133i	$-0.599921\pi$
$829$	−14740.5			−0.617562			−0.308781	+	0.951133i	$0.599921\pi$
$830$		0			0
$831$		−	14672.3i		−	0.612486i
$832$		0			0
$833$	−1120.01	+	12578.5i	−0.0465859	+	0.523194i
$834$		0			0
$835$			34257.7i			1.41981i
$836$		0			0
$837$	−44960.8			−1.85672
$838$		0			0
$839$	−8464.19	+	8464.19i	−0.348291	+	0.348291i	−0.859473	−	0.511182i	$-0.829208\pi$
$839$	−8464.19	+	8464.19i	−0.348291	+	0.348291i	0.511182	+	0.859473i	$0.329208\pi$
$840$		0			0
$841$		−	4022.69i		−	0.164939i
$842$		0			0
$843$	17798.5	−	17798.5i	0.727182	−	0.727182i
$844$		0			0
$845$	19055.2	+	19055.2i	0.775762	+	0.775762i
$846$		0			0
$847$	−15528.2	−	15528.2i	−0.629934	−	0.629934i
$848$		0			0
$849$	33530.7			1.35544
$850$		0			0
$851$	6423.40			0.258744
$852$		0			0
$853$	−19959.8	−	19959.8i	−0.801185	−	0.801185i	0.182096	−	0.983281i	$-0.441712\pi$
$853$	−19959.8	−	19959.8i	−0.801185	−	0.801185i	−0.983281	+	0.182096i	$0.941712\pi$
$854$		0			0
$855$	−3520.27	−	3520.27i	−0.140808	−	0.140808i
$856$		0			0
$857$	2185.79	−	2185.79i	0.0871238	−	0.0871238i	−0.662202	−	0.749326i	$-0.730378\pi$
$857$	2185.79	−	2185.79i	0.0871238	−	0.0871238i	0.749326	+	0.662202i	$0.230378\pi$
$858$		0			0
$859$		−	21827.6i		−	0.866994i	−0.901155	−	0.433497i	$-0.857280\pi$
$859$		−	21827.6i		−	0.866994i	0.901155	−	0.433497i	$-0.142720\pi$
$860$		0			0
$861$	7056.14	−	7056.14i	0.279295	−	0.279295i
$862$		0			0
$863$	12268.5			0.483921			0.241960	−	0.970286i	$-0.422210\pi$
$863$	12268.5			0.483921			0.241960	+	0.970286i	$0.422210\pi$
$864$		0			0
$865$		−	52327.7i		−	2.05687i
$866$		0			0
$867$	12194.5	+	17530.3i	0.477678	+	0.686689i
$868$		0			0
$869$		−	35052.8i		−	1.36834i
$870$		0			0
$871$	91.2672			0.00355048
$872$		0			0
$873$	1820.83	−	1820.83i	0.0705908	−	0.0705908i
$874$		0			0
$875$			15570.6i			0.601578i
$876$		0			0
$877$	−13528.2	+	13528.2i	−0.520883	+	0.520883i	−0.917838	−	0.396955i	$-0.870067\pi$
$877$	−13528.2	+	13528.2i	−0.520883	+	0.520883i	0.396955	+	0.917838i	$0.370067\pi$
$878$		0			0
$879$	−15344.4	−	15344.4i	−0.588800	−	0.588800i
$880$		0			0
$881$	−4803.46	−	4803.46i	−0.183692	−	0.183692i	0.609270	−	0.792962i	$-0.291462\pi$
$881$	−4803.46	−	4803.46i	−0.183692	−	0.183692i	−0.792962	+	0.609270i	$0.791462\pi$
$882$		0			0
$883$	−28197.9			−1.07467			−0.537335	−	0.843369i	$-0.680569\pi$
$883$	−28197.9			−1.07467			−0.537335	+	0.843369i	$0.680569\pi$
$884$		0			0
$885$	28761.1			1.09242
$886$		0			0
$887$	16408.3	+	16408.3i	0.621126	+	0.621126i	0.945819	−	0.324694i	$-0.105261\pi$
$887$	16408.3	+	16408.3i	0.621126	+	0.621126i	−0.324694	+	0.945819i	$0.605261\pi$
$888$		0			0
$889$	−8623.08	−	8623.08i	−0.325319	−	0.325319i
$890$		0			0
$891$	17358.4	−	17358.4i	0.652668	−	0.652668i
$892$		0			0
$893$		−	4634.14i		−	0.173657i
$894$		0			0
$895$	7734.53	−	7734.53i	0.288868	−	0.288868i
$896$		0			0
$897$	184.926			0.00688351
$898$		0			0
$899$		−	42048.0i		−	1.55993i
$900$		0			0
$901$	−2863.64	+	32160.8i	−0.105884	+	1.18916i
$902$		0			0
$903$		−	15217.1i		−	0.560791i
$904$		0			0
$905$	26821.4			0.985164
$906$		0			0
$907$	−10692.8	+	10692.8i	−0.391455	+	0.391455i	−0.875206	−	0.483751i	$-0.839274\pi$
$907$	−10692.8	+	10692.8i	−0.391455	+	0.391455i	0.483751	+	0.875206i	$0.339274\pi$
$908$		0			0
$909$		−	13719.7i		−	0.500608i
$910$		0			0
$911$	2425.45	−	2425.45i	0.0882095	−	0.0882095i	−0.661625	−	0.749835i	$-0.730133\pi$
$911$	2425.45	−	2425.45i	0.0882095	−	0.0882095i	0.749835	+	0.661625i	$0.230133\pi$
$912$		0			0
$913$	10317.6	+	10317.6i	0.374001	+	0.374001i
$914$		0			0
$915$	24337.9	+	24337.9i	0.879328	+	0.879328i
$916$		0			0
$917$	13999.1			0.504133
$918$		0			0
$919$	−53382.8			−1.91614			−0.958071	−	0.286530i	$-0.907498\pi$
$919$	−53382.8			−1.91614			−0.958071	+	0.286530i	$0.907498\pi$
$920$		0			0
$921$	−22823.2	−	22823.2i	−0.816559	−	0.816559i
$922$		0			0
$923$	49.9328	+	49.9328i	0.00178067	+	0.00178067i
$924$		0			0
$925$	2369.11	−	2369.11i	0.0842117	−	0.0842117i
$926$		0			0
$927$		−	5210.13i		−	0.184599i
$928$		0			0
$929$	−1215.07	+	1215.07i	−0.0429119	+	0.0429119i	−0.728237	−	0.685325i	$-0.759660\pi$
$929$	−1215.07	+	1215.07i	−0.0429119	+	0.0429119i	0.685325	+	0.728237i	$0.259660\pi$
$930$		0			0
$931$	−9016.20			−0.317394
$932$		0			0
$933$			37778.5i			1.32563i
$934$		0			0
$935$	−47325.2	−	4213.90i	−1.65530	−	0.147390i
$936$		0			0
$937$		−	11129.8i		−	0.388040i	−0.980998	−	0.194020i	$-0.937847\pi$
$937$		−	11129.8i		−	0.388040i	0.980998	−	0.194020i	$-0.0621527\pi$
$938$		0			0
$939$	−15648.4			−0.543839
$940$		0			0
$941$	2133.89	−	2133.89i	0.0739242	−	0.0739242i	−0.669178	−	0.743102i	$-0.733354\pi$
$941$	2133.89	−	2133.89i	0.0739242	−	0.0739242i	0.743102	+	0.669178i	$0.233354\pi$
$942$		0			0
$943$			8814.63i			0.304394i
$944$		0			0
$945$	−16894.7	+	16894.7i	−0.581571	+	0.581571i
$946$		0			0
$947$	13784.2	+	13784.2i	0.472994	+	0.472994i	0.902882	−	0.429888i	$-0.141447\pi$
$947$	13784.2	+	13784.2i	0.472994	+	0.472994i	−0.429888	+	0.902882i	$0.641447\pi$
$948$		0			0
$949$	−553.009	−	553.009i	−0.0189162	−	0.0189162i
$950$		0			0
$951$	−15181.9			−0.517674
$952$		0			0
$953$	−4535.38			−0.154161			−0.0770805	−	0.997025i	$-0.524560\pi$
$953$	−4535.38			−0.154161			−0.0770805	+	0.997025i	$0.524560\pi$
$954$		0			0
$955$	−16809.0	−	16809.0i	−0.569555	−	0.569555i
$956$		0			0
$957$	24231.0	+	24231.0i	0.818472	+	0.818472i
$958$		0			0
$959$	−4834.43	+	4834.43i	−0.162786	+	0.162786i
$960$		0			0
$961$			57020.7i			1.91402i
$962$		0			0
$963$	9634.63	−	9634.63i	0.322400	−	0.322400i
$964$		0			0
$965$	33140.6			1.10553
$966$		0			0
$967$		−	52772.2i		−	1.75495i	−0.479620	−	0.877476i	$-0.659226\pi$
$967$		−	52772.2i		−	1.75495i	0.479620	−	0.877476i	$-0.340774\pi$
$968$		0			0
$969$	−11694.5	+	9782.22i	−0.387701	+	0.324304i
$970$		0			0
$971$			16848.4i			0.556839i	0.960460	+	0.278420i	$0.0898106\pi$
$971$			16848.4i			0.556839i	−0.960460	+	0.278420i	$0.910189\pi$
$972$		0			0
$973$	10022.0			0.330206
$974$		0			0
$975$	68.2054	−	68.2054i	0.00224033	−	0.00224033i
$976$		0			0
$977$			24152.4i			0.790893i	0.918489	+	0.395447i	$0.129410\pi$
$977$			24152.4i			0.790893i	−0.918489	+	0.395447i	$0.870590\pi$
$978$		0			0
$979$	−61474.1	+	61474.1i	−2.00686	+	2.00686i
$980$		0			0
$981$	4269.18	+	4269.18i	0.138944	+	0.138944i
$982$		0			0
$983$	22057.4	+	22057.4i	0.715689	+	0.715689i	0.967719	−	0.252030i	$-0.0810982\pi$
$983$	22057.4	+	22057.4i	0.715689	+	0.715689i	−0.252030	+	0.967719i	$0.581098\pi$
$984$		0			0
$985$	−6927.38			−0.224086
$986$		0			0
$987$	−5136.11			−0.165637
$988$		0			0
$989$	9504.73	+	9504.73i	0.305594	+	0.305594i
$990$		0			0
$991$	8193.28	+	8193.28i	0.262632	+	0.262632i	0.826122	−	0.563491i	$-0.190542\pi$
$991$	8193.28	+	8193.28i	0.262632	+	0.262632i	−0.563491	+	0.826122i	$0.690542\pi$
$992$		0			0
$993$	15652.0	−	15652.0i	0.500204	−	0.500204i
$994$		0			0
$995$			63306.9i			2.01705i
$996$		0			0
$997$	−347.648	+	347.648i	−0.0110432	+	0.0110432i	−0.712607	−	0.701564i	$-0.752486\pi$
$997$	−347.648	+	347.648i	−0.0110432	+	0.0110432i	0.701564	+	0.712607i	$0.252486\pi$
$998$		0			0
$999$	−20006.5			−0.633611

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.4.k.a.81.5	✓	14
4.3	odd	2		272.4.o.g.81.3		14
17.2	even	8		2312.4.a.m.1.10		14
17.4	even	4	inner	136.4.k.a.89.5	yes	14
17.15	even	8		2312.4.a.m.1.5		14
68.55	odd	4		272.4.o.g.225.3		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.4.k.a.81.5	✓	14	1.1	even	1	trivial
136.4.k.a.89.5	yes	14	17.4	even	4	inner
272.4.o.g.81.3		14	4.3	odd	2
272.4.o.g.225.3		14	68.55	odd	4
2312.4.a.m.1.5		14	17.15	even	8
2312.4.a.m.1.10		14	17.2	even	8

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:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	136.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.07347 + 3.07347i) q^{3} +(-8.67626 - 8.67626i) q^{5} +(9.02315 - 9.02315i) q^{7} -8.10760i q^{9} +O(q^{10})\)	\(q+(3.07347 + 3.07347i) q^{3} +(-8.67626 - 8.67626i) q^{5} +(9.02315 - 9.02315i) q^{7} -8.10760i q^{9} +(39.0636 - 39.0636i) q^{11} -0.868393 q^{13} -53.3324i q^{15} +(69.8166 + 6.21656i) q^{17} +50.0440i q^{19} +55.4647 q^{21} +(-34.6437 + 34.6437i) q^{23} +25.5549i q^{25} +(107.902 - 107.902i) q^{27} +(100.912 + 100.912i) q^{29} +(-208.341 - 208.341i) q^{31} +240.121 q^{33} -156.574 q^{35} +(-92.7068 - 92.7068i) q^{37} +(-2.66898 - 2.66898i) q^{39} +(127.219 - 127.219i) q^{41} -274.357i q^{43} +(-70.3436 + 70.3436i) q^{45} -92.6014 q^{47} +180.166i q^{49} +(195.473 + 233.685i) q^{51} +460.648i q^{53} -677.851 q^{55} +(-153.808 + 153.808i) q^{57} +539.280i q^{59} +(-456.343 + 456.343i) q^{61} +(-73.1561 - 73.1561i) q^{63} +(7.53440 + 7.53440i) q^{65} -105.099 q^{67} -212.952 q^{69} +(-57.5002 - 57.5002i) q^{71} +(636.819 + 636.819i) q^{73} +(-78.5421 + 78.5421i) q^{75} -704.953i q^{77} +(448.664 - 448.664i) q^{79} +444.362 q^{81} +264.124i q^{83} +(-551.810 - 659.683i) q^{85} +620.297i q^{87} -1573.69 q^{89} +(-7.83564 + 7.83564i) q^{91} -1280.66i q^{93} +(434.194 - 434.194i) q^{95} +(224.583 + 224.583i) q^{97} +(-316.712 - 316.712i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 4 q^{3} + 8 q^{5} - 10 q^{7}+O(q^{10}) \) 14 * q - 4 * q^3 + 8 * q^5 - 10 * q^7	\( 14 q - 4 q^{3} + 8 q^{5} - 10 q^{7} + 16 q^{11} + 72 q^{13} - 40 q^{17} - 60 q^{21} + 246 q^{23} + 572 q^{27} + 260 q^{29} + 566 q^{31} - 904 q^{33} - 804 q^{35} - 28 q^{37} + 476 q^{39} - 786 q^{41} - 604 q^{45} + 448 q^{47} - 380 q^{51} + 1612 q^{55} + 1004 q^{57} + 660 q^{61} - 2250 q^{63} - 796 q^{65} - 284 q^{67} - 2532 q^{69} + 326 q^{71} + 730 q^{73} - 864 q^{75} + 342 q^{79} - 950 q^{81} + 4148 q^{85} - 4516 q^{89} - 3112 q^{91} + 3356 q^{95} - 1194 q^{97} + 2876 q^{99}+O(q^{100}) \) 14 * q - 4 * q^3 + 8 * q^5 - 10 * q^7 + 16 * q^11 + 72 * q^13 - 40 * q^17 - 60 * q^21 + 246 * q^23 + 572 * q^27 + 260 * q^29 + 566 * q^31 - 904 * q^33 - 804 * q^35 - 28 * q^37 + 476 * q^39 - 786 * q^41 - 604 * q^45 + 448 * q^47 - 380 * q^51 + 1612 * q^55 + 1004 * q^57 + 660 * q^61 - 2250 * q^63 - 796 * q^65 - 284 * q^67 - 2532 * q^69 + 326 * q^71 + 730 * q^73 - 864 * q^75 + 342 * q^79 - 950 * q^81 + 4148 * q^85 - 4516 * q^89 - 3112 * q^91 + 3356 * q^95 - 1194 * q^97 + 2876 * q^99

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