LMFDB - Embedded newform 350.8.c.i.99.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,8,Mod(99,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("350.99");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	350.c (of order $2$, degree $1$, 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:	$109.334758919$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{8761})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 4381x^{2} + 4796100 $ x^4 + 4381*x^2 + 4796100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.3
Root			$-46.3001i$ of defining polynomial
Character	$\chi$	$=$	350.99
Dual form			350.8.c.i.99.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+8.00000i q^{2} -44.3001i q^{3} -64.0000 q^{4} +354.401 q^{6} +343.000i q^{7} -512.000i q^{8} +224.501 q^{9} +O(q^{10})$	\(q+8.00000i q^{2} -44.3001i q^{3} -64.0000 q^{4} +354.401 q^{6} +343.000i q^{7} -512.000i q^{8} +224.501 q^{9} +8294.71 q^{11} +2835.21i q^{12} -2086.69i q^{13} -2744.00 q^{14} +4096.00 q^{16} +22276.5i q^{17} +1796.00i q^{18} -22693.4 q^{19} +15194.9 q^{21} +66357.7i q^{22} +51846.8i q^{23} -22681.7 q^{24} +16693.6 q^{26} -106830. i q^{27} -21952.0i q^{28} +69360.5 q^{29} +54654.7 q^{31} +32768.0i q^{32} -367457. i q^{33} -178212. q^{34} -14368.0 q^{36} +301929. i q^{37} -181547. i q^{38} -92440.8 q^{39} -120041. q^{41} +121559. i q^{42} +260607. i q^{43} -530862. q^{44} -414774. q^{46} -282025. i q^{47} -181453. i q^{48} -117649. q^{49} +986852. q^{51} +133548. i q^{52} -413071. i q^{53} +854638. q^{54} +175616. q^{56} +1.00532e6i q^{57} +554884. i q^{58} -961690. q^{59} -2.52312e6 q^{61} +437238. i q^{62} +77003.7i q^{63} -262144. q^{64} +2.93965e6 q^{66} -133835. i q^{67} -1.42570e6i q^{68} +2.29682e6 q^{69} -5.71568e6 q^{71} -114944. i q^{72} -28628.0i q^{73} -2.41543e6 q^{74} +1.45238e6 q^{76} +2.84509e6i q^{77} -739526. i q^{78} +7.61428e6 q^{79} -4.24159e6 q^{81} -960326. i q^{82} +2.64843e6i q^{83} -972476. q^{84} -2.08486e6 q^{86} -3.07268e6i q^{87} -4.24689e6i q^{88} +7.82855e6 q^{89} +715736. q^{91} -3.31819e6i q^{92} -2.42121e6i q^{93} +2.25620e6 q^{94} +1.45163e6 q^{96} +9.84758e6i q^{97} -941192. i q^{98} +1.86217e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 256 q^{4} - 80 q^{6} - 38 q^{9}+O(q^{10}) $ 4 * q - 256 * q^4 - 80 * q^6 - 38 * q^9	$ 4 q - 256 q^{4} - 80 q^{6} - 38 q^{9} + 9030 q^{11} - 10976 q^{14} + 16384 q^{16} - 87404 q^{19} - 3430 q^{21} + 5120 q^{24} + 143152 q^{26} - 18522 q^{29} + 414056 q^{31} - 600528 q^{34} + 2432 q^{36} + 491546 q^{39} + 529596 q^{41} - 577920 q^{44} + 650208 q^{46} - 470596 q^{49} + 469410 q^{51} + 176240 q^{54} + 702464 q^{56} - 3810816 q^{59} - 238636 q^{61} - 1048576 q^{64} + 8860752 q^{66} + 13712652 q^{69} - 1225344 q^{71} + 2289152 q^{74} + 5593856 q^{76} + 25241518 q^{79} - 18995596 q^{81} + 219520 q^{84} - 8402336 q^{86} + 22356660 q^{89} + 6137642 q^{91} + 8121744 q^{94} - 327680 q^{96} + 5565060 q^{99}+O(q^{100}) $ 4 * q - 256 * q^4 - 80 * q^6 - 38 * q^9 + 9030 * q^11 - 10976 * q^14 + 16384 * q^16 - 87404 * q^19 - 3430 * q^21 + 5120 * q^24 + 143152 * q^26 - 18522 * q^29 + 414056 * q^31 - 600528 * q^34 + 2432 * q^36 + 491546 * q^39 + 529596 * q^41 - 577920 * q^44 + 650208 * q^46 - 470596 * q^49 + 469410 * q^51 + 176240 * q^54 + 702464 * q^56 - 3810816 * q^59 - 238636 * q^61 - 1048576 * q^64 + 8860752 * q^66 + 13712652 * q^69 - 1225344 * q^71 + 2289152 * q^74 + 5593856 * q^76 + 25241518 * q^79 - 18995596 * q^81 + 219520 * q^84 - 8402336 * q^86 + 22356660 * q^89 + 6137642 * q^91 + 8121744 * q^94 - 327680 * q^96 + 5565060 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$-1$

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 $

$2$	8.00000i	0.707107i
$2$	8.00000i	0.707107i
$3$	− 44.3001i	− 0.947284i	−0.880717	−	0.473642i	$-0.842939\pi$
$3$	− 44.3001i	− 0.947284i	0.880717	−	0.473642i	$-0.157061\pi$
$4$	−64.0000	−0.500000
$5$	0	0
$5$	0	0
$6$	354.401	0.669831
$7$	343.000i	0.377964i
$7$	343.000i	0.377964i
$8$	− 512.000i	− 0.353553i
$9$	224.501	0.102652
$10$	0	0
$11$	8294.71	1.87900	0.939500	−	0.342548i	$-0.111290\pi$
$11$	8294.71	1.87900	0.939500	+	0.342548i	$0.111290\pi$
$12$	2835.21i	0.473642i
$13$	− 2086.69i	− 0.263425i	−0.991288	−	0.131713i	$-0.957952\pi$
$13$	− 2086.69i	− 0.263425i	0.991288	−	0.131713i	$-0.0420476\pi$
$14$	−2744.00	−0.267261
$15$	0	0
$16$	4096.00	0.250000
$17$	22276.5i	1.09970i	0.835262	+	0.549852i	$0.185316\pi$
$17$	22276.5i	1.09970i	−0.835262	+	0.549852i	$0.814684\pi$
$18$	1796.00i	0.0725861i
$19$	−22693.4	−0.759035	−0.379518	−	0.925184i	$-0.623910\pi$
$19$	−22693.4	−0.759035	−0.379518	+	0.925184i	$0.623910\pi$
$20$	0	0
$21$	15194.9	0.358040
$22$	66357.7i	1.32865i
$23$	51846.8i	0.888534i	0.895894	+	0.444267i	$0.146536\pi$
$23$	51846.8i	0.888534i	−0.895894	+	0.444267i	$0.853464\pi$
$24$	−22681.7	−0.334916
$25$	0	0
$26$	16693.6	0.186270
$27$	− 106830.i	− 1.04453i
$28$	− 21952.0i	− 0.188982i
$29$	69360.5	0.528103	0.264052	−	0.964509i	$-0.414941\pi$
$29$	69360.5	0.528103	0.264052	+	0.964509i	$0.414941\pi$
$30$	0	0
$31$	54654.7	0.329505	0.164752	−	0.986335i	$-0.447318\pi$
$31$	54654.7	0.329505	0.164752	+	0.986335i	$0.447318\pi$
$32$	32768.0i	0.176777i
$33$	− 367457.i	− 1.77995i
$34$	−178212.	−0.777608
$35$	0	0
$36$	−14368.0	−0.0513261
$37$	301929.i	0.979938i	0.871740	+	0.489969i	$0.162992\pi$
$37$	301929.i	0.979938i	−0.871740	+	0.489969i	$0.837008\pi$
$38$	− 181547.i	− 0.536719i
$39$	−92440.8	−0.249538
$40$	0	0
$41$	−120041.	−0.272010	−0.136005	−	0.990708i	$-0.543426\pi$
$41$	−120041.	−0.272010	−0.136005	+	0.990708i	$0.543426\pi$
$42$	121559.i	0.253172i
$43$	260607.i	0.499859i	0.968264	+	0.249929i	$0.0804074\pi$
$43$	260607.i	0.499859i	−0.968264	+	0.249929i	$0.919593\pi$
$44$	−530862.	−0.939500
$45$	0	0
$46$	−414774.	−0.628289
$47$	− 282025.i	− 0.396228i	−0.980179	−	0.198114i	$-0.936518\pi$
$47$	− 282025.i	− 0.396228i	0.980179	−	0.198114i	$-0.0634816\pi$
$48$	− 181453.i	− 0.236821i
$49$	−117649.	−0.142857
$50$	0	0
$51$	986852.	1.04173
$52$	133548.i	0.131713i
$53$	− 413071.i	− 0.381118i	−0.981676	−	0.190559i	$-0.938970\pi$
$53$	− 413071.i	− 0.381118i	0.981676	−	0.190559i	$-0.0610300\pi$
$54$	854638.	0.738591
$55$	0	0
$56$	175616.	0.133631
$57$	1.00532e6i	0.719022i
$58$	554884.i	0.373426i
$59$	−961690.	−0.609611	−0.304806	−	0.952415i	$-0.598591\pi$
$59$	−961690.	−0.609611	−0.304806	+	0.952415i	$0.598591\pi$
$60$	0	0
$61$	−2.52312e6	−1.42326	−0.711630	−	0.702555i	$-0.752043\pi$
$61$	−2.52312e6	−1.42326	−0.711630	+	0.702555i	$0.752043\pi$
$62$	437238.i	0.232995i
$63$	77003.7i	0.0387989i
$64$	−262144.	−0.125000
$65$	0	0
$66$	2.93965e6	1.25861
$67$	− 133835.i	− 0.0543637i	−0.999631	−	0.0271819i	$-0.991347\pi$
$67$	− 133835.i	− 0.0543637i	0.999631	−	0.0271819i	$-0.00865332\pi$
$68$	− 1.42570e6i	− 0.549852i
$69$	2.29682e6	0.841695
$70$	0	0
$71$	−5.71568e6	−1.89524	−0.947619	−	0.319404i	$-0.896517\pi$
$71$	−5.71568e6	−1.89524	−0.947619	+	0.319404i	$0.896517\pi$
$72$	− 114944.i	− 0.0362931i
$73$	− 28628.0i	− 0.00861314i	−0.999991	−	0.00430657i	$-0.998629\pi$
$73$	− 28628.0i	− 0.00861314i	0.999991	−	0.00430657i	$-0.00137083\pi$
$74$	−2.41543e6	−0.692921
$75$	0	0
$76$	1.45238e6	0.379518
$77$	2.84509e6i	0.710196i
$78$	− 739526.i	− 0.176450i
$79$	7.61428e6	1.73754	0.868768	−	0.495219i	$-0.164912\pi$
$79$	7.61428e6	1.73754	0.868768	+	0.495219i	$0.164912\pi$
$80$	0	0
$81$	−4.24159e6	−0.886810
$82$	− 960326.i	− 0.192340i
$83$	2.64843e6i	0.508411i	0.967150	+	0.254206i	$0.0818140\pi$
$83$	2.64843e6i	0.508411i	−0.967150	+	0.254206i	$0.918186\pi$
$84$	−972476.	−0.179020
$85$	0	0
$86$	−2.08486e6	−0.353453
$87$	− 3.07268e6i	− 0.500264i
$88$	− 4.24689e6i	− 0.664327i
$89$	7.82855e6	1.17711	0.588554	−	0.808458i	$-0.299697\pi$
$89$	7.82855e6	1.17711	0.588554	+	0.808458i	$0.299697\pi$
$90$	0	0
$91$	715736.	0.0995653
$92$	− 3.31819e6i	− 0.444267i
$93$	− 2.42121e6i	− 0.312135i
$94$	2.25620e6	0.280175
$95$	0	0
$96$	1.45163e6	0.167458
$97$	9.84758e6i	1.09554i	0.836629	+	0.547770i	$0.184523\pi$
$97$	9.84758e6i	1.09554i	−0.836629	+	0.547770i	$0.815477\pi$
$98$	− 941192.i	− 0.101015i
$99$	1.86217e6	0.192884
$100$	0	0
$101$	1.89329e7	1.82848	0.914242	−	0.405168i	$-0.132787\pi$
$101$	1.89329e7	1.82848	0.914242	+	0.405168i	$0.132787\pi$
$102$	7.89481e6i	0.736616i
$103$	1.88723e7i	1.70174i	0.525374	+	0.850871i	$0.323925\pi$
$103$	1.88723e7i	1.70174i	−0.525374	+	0.850871i	$0.676075\pi$
$104$	−1.06839e6	−0.0931348
$105$	0	0
$106$	3.30457e6	0.269491
$107$	− 1.75676e6i	− 0.138634i	−0.997595	−	0.0693168i	$-0.977918\pi$
$107$	− 1.75676e6i	− 0.138634i	0.997595	−	0.0693168i	$-0.0220819\pi$
$108$	6.83710e6i	0.522263i
$109$	1.51030e7	1.11704	0.558521	−	0.829490i	$-0.311369\pi$
$109$	1.51030e7	1.11704	0.558521	+	0.829490i	$0.311369\pi$
$110$	0	0
$111$	1.33755e7	0.928280
$112$	1.40493e6i	0.0944911i
$113$	9.05559e6i	0.590394i	0.955436	+	0.295197i	$0.0953854\pi$
$113$	9.05559e6i	0.590394i	−0.955436	+	0.295197i	$0.904615\pi$
$114$	−8.04256e6	−0.508426
$115$	0	0
$116$	−4.43907e6	−0.264052
$117$	− 468464.i	− 0.0270412i
$118$	− 7.69352e6i	− 0.431060i
$119$	−7.64084e6	−0.415649
$120$	0	0
$121$	4.93151e7	2.53064
$122$	− 2.01850e7i	− 1.00640i
$123$	5.31782e6i	0.257671i
$124$	−3.49790e6	−0.164752
$125$	0	0
$126$	−616029.	−0.0274350
$127$	3.51254e7i	1.52163i	0.648971	+	0.760813i	$0.275200\pi$
$127$	3.51254e7i	1.52163i	−0.648971	+	0.760813i	$0.724800\pi$
$128$	− 2.09715e6i	− 0.0883883i
$129$	1.15449e7	0.473508
$130$	0	0
$131$	4.78958e7	1.86143	0.930717	−	0.365740i	$-0.119184\pi$
$131$	4.78958e7	1.86143	0.930717	+	0.365740i	$0.119184\pi$
$132$	2.35172e7i	0.889974i
$133$	− 7.78384e6i	− 0.286888i
$134$	1.07068e6	0.0384409
$135$	0	0
$136$	1.14056e7	0.388804
$137$	− 3.21903e6i	− 0.106955i	−0.998569	−	0.0534777i	$-0.982969\pi$
$137$	− 3.21903e6i	− 0.106955i	0.998569	−	0.0534777i	$-0.0170306\pi$
$138$	1.83745e7i	0.595168i
$139$	−2.92523e7	−0.923866	−0.461933	−	0.886915i	$-0.652844\pi$
$139$	−2.92523e7	−0.923866	−0.461933	+	0.886915i	$0.652844\pi$
$140$	0	0
$141$	−1.24937e7	−0.375341
$142$	− 4.57254e7i	− 1.34014i
$143$	− 1.73085e7i	− 0.494976i
$144$	919554.	0.0256631
$145$	0	0
$146$	229024.	0.00609041
$147$	5.21186e6i	0.135326i
$148$	− 1.93234e7i	− 0.489969i
$149$	−2.12164e7	−0.525436	−0.262718	−	0.964873i	$-0.584619\pi$
$149$	−2.12164e7	−0.525436	−0.262718	+	0.964873i	$0.584619\pi$
$150$	0	0
$151$	−2.71361e7	−0.641398	−0.320699	−	0.947181i	$-0.603918\pi$
$151$	−2.71361e7	−0.641398	−0.320699	+	0.947181i	$0.603918\pi$
$152$	1.16190e7i	0.268360i
$153$	5.00109e6i	0.112887i
$154$	−2.27607e7	−0.502184
$155$	0	0
$156$	5.91621e6	0.124769
$157$	− 1.51261e7i	− 0.311944i	−0.987761	−	0.155972i	$-0.950149\pi$
$157$	− 1.51261e7i	− 0.311944i	0.987761	−	0.155972i	$-0.0498510\pi$
$158$	6.09142e7i	1.22862i
$159$	−1.82991e7	−0.361027
$160$	0	0
$161$	−1.77834e7	−0.335834
$162$	− 3.39327e7i	− 0.627070i
$163$	1.01081e8i	1.82816i	0.405536	+	0.914079i	$0.367085\pi$
$163$	1.01081e8i	1.82816i	−0.405536	+	0.914079i	$0.632915\pi$
$164$	7.68261e6	0.136005
$165$	0	0
$166$	−2.11874e7	−0.359501
$167$	− 4.83737e7i	− 0.803714i	−0.915702	−	0.401857i	$-0.868365\pi$
$167$	− 4.83737e7i	− 0.803714i	0.915702	−	0.401857i	$-0.131635\pi$
$168$	− 7.77981e6i	− 0.126586i
$169$	5.83942e7	0.930607
$170$	0	0
$171$	−5.09468e6	−0.0779167
$172$	− 1.66789e7i	− 0.249929i
$173$	− 6.02289e6i	− 0.0884390i	−0.999022	−	0.0442195i	$-0.985920\pi$
$173$	− 6.02289e6i	− 0.0884390i	0.999022	−	0.0442195i	$-0.0140801\pi$
$174$	2.45814e7	0.353740
$175$	0	0
$176$	3.39751e7	0.469750
$177$	4.26030e7i	0.577475i
$178$	6.26284e7i	0.832341i
$179$	1.04527e7	0.136221	0.0681103	−	0.997678i	$-0.478303\pi$
$179$	1.04527e7	0.136221	0.0681103	+	0.997678i	$0.478303\pi$
$180$	0	0
$181$	1.01810e8	1.27619	0.638095	−	0.769958i	$-0.279723\pi$
$181$	1.01810e8	1.27619	0.638095	+	0.769958i	$0.279723\pi$
$182$	5.72589e6i	0.0704033i
$183$	1.11775e8i	1.34823i
$184$	2.65455e7	0.314144
$185$	0	0
$186$	1.93697e7	0.220712
$187$	1.84777e8i	2.06635i
$188$	1.80496e7i	0.198114i
$189$	3.66426e7	0.394793
$190$	0	0
$191$	1.16808e8	1.21299	0.606495	−	0.795088i	$-0.292575\pi$
$191$	1.16808e8	1.21299	0.606495	+	0.795088i	$0.292575\pi$
$192$	1.16130e7i	0.118411i
$193$	1.72514e8i	1.72732i	0.504073	+	0.863661i	$0.331834\pi$
$193$	1.72514e8i	1.72732i	−0.504073	+	0.863661i	$0.668166\pi$
$194$	−7.87807e7	−0.774664
$195$	0	0
$196$	7.52954e6	0.0714286
$197$	− 1.13246e8i	− 1.05534i	−0.849450	−	0.527669i	$-0.823066\pi$
$197$	− 1.13246e8i	− 1.05534i	0.849450	−	0.527669i	$-0.176934\pi$
$198$	1.48973e7i	0.136389i
$199$	−1.87994e8	−1.69106	−0.845529	−	0.533930i	$-0.820715\pi$
$199$	−1.87994e8	−1.69106	−0.845529	+	0.533930i	$0.820715\pi$
$200$	0	0
$201$	−5.92892e6	−0.0514979
$202$	1.51463e8i	1.29293i
$203$	2.37906e7i	0.199604i
$204$	−6.31585e7	−0.520866
$205$	0	0
$206$	−1.50978e8	−1.20331
$207$	1.16396e7i	0.0912101i
$208$	− 8.54710e6i	− 0.0658563i
$209$	−1.88235e8	−1.42623
$210$	0	0
$211$	−2.04724e7	−0.150031	−0.0750155	−	0.997182i	$-0.523901\pi$
$211$	−2.04724e7	−0.150031	−0.0750155	+	0.997182i	$0.523901\pi$
$212$	2.64365e7i	0.190559i
$213$	2.53205e8i	1.79533i
$214$	1.40541e7	0.0980287
$215$	0	0
$216$	−5.46968e7	−0.369295
$217$	1.87466e7i	0.124541i
$218$	1.20824e8i	0.789868i
$219$	−1.26823e6	−0.00815910
$220$	0	0
$221$	4.64843e7	0.289690
$222$	1.07004e8i	0.656393i
$223$	− 1.96181e8i	− 1.18465i	−0.805698	−	0.592326i	$-0.798210\pi$
$223$	− 1.96181e8i	− 1.18465i	0.805698	−	0.592326i	$-0.201790\pi$
$224$	−1.12394e7	−0.0668153
$225$	0	0
$226$	−7.24447e7	−0.417472
$227$	9.92114e7i	0.562951i	0.959568	+	0.281476i	$0.0908239\pi$
$227$	9.92114e7i	0.562951i	−0.959568	+	0.281476i	$0.909176\pi$
$228$	− 6.43405e7i	− 0.359511i
$229$	−2.80737e7	−0.154481	−0.0772407	−	0.997012i	$-0.524611\pi$
$229$	−2.80737e7	−0.154481	−0.0772407	+	0.997012i	$0.524611\pi$
$230$	0	0
$231$	1.26038e8	0.672757
$232$	− 3.55126e7i	− 0.186713i
$233$	2.59746e7i	0.134525i	0.997735	+	0.0672626i	$0.0214265\pi$
$233$	2.59746e7i	0.134525i	−0.997735	+	0.0672626i	$0.978573\pi$
$234$	3.74771e6	0.0191210
$235$	0	0
$236$	6.15481e7	0.304806
$237$	− 3.37313e8i	− 1.64594i
$238$	− 6.11267e7i	− 0.293908i
$239$	2.89625e8	1.37228	0.686142	−	0.727468i	$-0.259303\pi$
$239$	2.89625e8	1.37228	0.686142	+	0.727468i	$0.259303\pi$
$240$	0	0
$241$	−2.35224e8	−1.08248	−0.541242	−	0.840867i	$-0.682046\pi$
$241$	−2.35224e8	−1.08248	−0.541242	+	0.840867i	$0.682046\pi$
$242$	3.94521e8i	1.78944i
$243$	− 4.57339e7i	− 0.204464i
$244$	1.61480e8	0.711630
$245$	0	0
$246$	−4.25426e7	−0.182201
$247$	4.73542e7i	0.199949i
$248$	− 2.79832e7i	− 0.116497i
$249$	1.17326e8	0.481610
$250$	0	0
$251$	3.71067e8	1.48113	0.740566	−	0.671984i	$-0.234558\pi$
$251$	3.71067e8	1.48113	0.740566	+	0.671984i	$0.234558\pi$
$252$	− 4.92824e6i	− 0.0193995i
$253$	4.30054e8i	1.66956i
$254$	−2.81003e8	−1.07595
$255$	0	0
$256$	1.67772e7	0.0625000
$257$	2.53506e8i	0.931585i	0.884894	+	0.465792i	$0.154231\pi$
$257$	2.53506e8i	0.931585i	−0.884894	+	0.465792i	$0.845769\pi$
$258$	9.23595e7i	0.334821i
$259$	−1.03562e8	−0.370382
$260$	0	0
$261$	1.55715e7	0.0542110
$262$	3.83166e8i	1.31623i
$263$	− 3.39492e8i	− 1.15076i	−0.817887	−	0.575379i	$-0.804855\pi$
$263$	− 3.39492e8i	− 1.15076i	0.817887	−	0.575379i	$-0.195145\pi$
$264$	−1.88138e8	−0.629307
$265$	0	0
$266$	6.22707e7	0.202861
$267$	− 3.46806e8i	− 1.11506i
$268$	8.56546e6i	0.0271819i
$269$	−1.51784e8	−0.475436	−0.237718	−	0.971334i	$-0.576399\pi$
$269$	−1.51784e8	−0.475436	−0.237718	+	0.971334i	$0.576399\pi$
$270$	0	0
$271$	6.09610e7	0.186063	0.0930314	−	0.995663i	$-0.470344\pi$
$271$	6.09610e7	0.186063	0.0930314	+	0.995663i	$0.470344\pi$
$272$	9.12446e7i	0.274926i
$273$	− 3.17072e7i	− 0.0943167i
$274$	2.57522e7	0.0756289
$275$	0	0
$276$	−1.46996e8	−0.420847
$277$	− 2.27766e8i	− 0.643888i	−0.946759	−	0.321944i	$-0.895664\pi$
$277$	− 2.27766e8i	− 0.643888i	0.946759	−	0.321944i	$-0.104336\pi$
$278$	− 2.34019e8i	− 0.653272i
$279$	1.22700e7	0.0338244
$280$	0	0
$281$	4.86914e8	1.30912	0.654560	−	0.756010i	$-0.272854\pi$
$281$	4.86914e8	1.30912	0.654560	+	0.756010i	$0.272854\pi$
$282$	− 9.99499e7i	− 0.265406i
$283$	2.62185e8i	0.687631i	0.939037	+	0.343815i	$0.111719\pi$
$283$	2.62185e8i	0.687631i	−0.939037	+	0.343815i	$0.888281\pi$
$284$	3.65803e8	0.947619
$285$	0	0
$286$	1.38468e8	0.350001
$287$	− 4.11740e7i	− 0.102810i
$288$	7.35643e6i	0.0181465i
$289$	−8.59041e7	−0.209349
$290$	0	0
$291$	4.36249e8	1.03779
$292$	1.83219e6i	0.00430657i
$293$	− 7.42829e7i	− 0.172525i	−0.996272	−	0.0862625i	$-0.972508\pi$
$293$	− 7.42829e7i	− 0.172525i	0.996272	−	0.0862625i	$-0.0274924\pi$
$294$	−4.16949e7	−0.0956902
$295$	0	0
$296$	1.54588e8	0.346460
$297$	− 8.86122e8i	− 1.96266i
$298$	− 1.69731e8i	− 0.371539i
$299$	1.08188e8	0.234062
$300$	0	0
$301$	−8.93883e7	−0.188929
$302$	− 2.17089e8i	− 0.453537i
$303$	− 8.38728e8i	− 1.73210i
$304$	−9.29522e7	−0.189759
$305$	0	0
$306$	−4.00087e7	−0.0798233
$307$	− 4.64592e8i	− 0.916404i	−0.888848	−	0.458202i	$-0.848494\pi$
$307$	− 4.64592e8i	− 0.916404i	0.888848	−	0.458202i	$-0.151506\pi$
$308$	− 1.82086e8i	− 0.355098i
$309$	8.36043e8	1.61203
$310$	0	0
$311$	−6.84752e8	−1.29084	−0.645419	−	0.763829i	$-0.723317\pi$
$311$	−6.84752e8	−1.29084	−0.645419	+	0.763829i	$0.723317\pi$
$312$	4.73297e7i	0.0882252i
$313$	2.85953e8i	0.527096i	0.964646	+	0.263548i	$0.0848927\pi$
$313$	2.85953e8i	0.527096i	−0.964646	+	0.263548i	$0.915107\pi$
$314$	1.21009e8	0.220578
$315$	0	0
$316$	−4.87314e8	−0.868768
$317$	8.17943e8i	1.44217i	0.692848	+	0.721084i	$0.256356\pi$
$317$	8.17943e8i	1.44217i	−0.692848	+	0.721084i	$0.743644\pi$
$318$	− 1.46393e8i	− 0.255284i
$319$	5.75325e8	0.992307
$320$	0	0
$321$	−7.78245e7	−0.131325
$322$	− 1.42268e8i	− 0.237471i
$323$	− 5.05530e8i	− 0.834714i
$324$	2.71461e8	0.443405
$325$	0	0
$326$	−8.08649e8	−1.29270
$327$	− 6.69063e8i	− 1.05816i
$328$	6.14609e7i	0.0961702i
$329$	9.67346e7	0.149760
$330$	0	0
$331$	9.47073e8	1.43544	0.717720	−	0.696331i	$-0.245186\pi$
$331$	9.47073e8	1.43544	0.717720	+	0.696331i	$0.245186\pi$
$332$	− 1.69499e8i	− 0.254206i
$333$	6.77832e7i	0.100593i
$334$	3.86990e8	0.568312
$335$	0	0
$336$	6.22385e7	0.0895100
$337$	− 1.36535e9i	− 1.94330i	−0.236415	−	0.971652i	$-0.575973\pi$
$337$	− 1.36535e9i	− 1.94330i	0.236415	−	0.971652i	$-0.424027\pi$
$338$	4.67154e8i	0.658039i
$339$	4.01164e8	0.559271
$340$	0	0
$341$	4.53345e8	0.619139
$342$	− 4.07574e7i	− 0.0550954i
$343$	− 4.03536e7i	− 0.0539949i
$344$	1.33431e8	0.176727
$345$	0	0
$346$	4.81831e7	0.0625358
$347$	9.66351e8i	1.24160i	0.783969	+	0.620800i	$0.213192\pi$
$347$	9.66351e8i	1.24160i	−0.783969	+	0.620800i	$0.786808\pi$
$348$	1.96651e8i	0.250132i
$349$	−6.50882e8	−0.819621	−0.409811	−	0.912171i	$-0.634405\pi$
$349$	−6.50882e8	−0.819621	−0.409811	+	0.912171i	$0.634405\pi$
$350$	0	0
$351$	−2.22921e8	−0.275154
$352$	2.71801e8i	0.332164i
$353$	− 6.03836e8i	− 0.730647i	−0.930881	−	0.365323i	$-0.880958\pi$
$353$	− 6.03836e8i	− 0.730647i	0.930881	−	0.365323i	$-0.119042\pi$
$354$	−3.40824e8	−0.408337
$355$	0	0
$356$	−5.01027e8	−0.588554
$357$	3.38490e8i	0.393738i
$358$	8.36216e7i	0.0963225i
$359$	−8.56904e7	−0.0977466	−0.0488733	−	0.998805i	$-0.515563\pi$
$359$	−8.56904e7	−0.0977466	−0.0488733	+	0.998805i	$0.515563\pi$
$360$	0	0
$361$	−3.78881e8	−0.423865
$362$	8.14480e8i	0.902403i
$363$	− 2.18466e9i	− 2.39724i
$364$	−4.58071e7	−0.0497827
$365$	0	0
$366$	−8.94197e8	−0.953343
$367$	− 1.63658e9i	− 1.72825i	−0.503276	−	0.864126i	$-0.667872\pi$
$367$	− 1.63658e9i	− 1.72825i	0.503276	−	0.864126i	$-0.332128\pi$
$368$	2.12364e8i	0.222134i
$369$	−2.69492e7	−0.0279225
$370$	0	0
$371$	1.41683e8	0.144049
$372$	1.54957e8i	0.156067i
$373$	1.88055e9i	1.87630i	0.346223	+	0.938152i	$0.387464\pi$
$373$	1.88055e9i	1.87630i	−0.346223	+	0.938152i	$0.612536\pi$
$374$	−1.47822e9	−1.46113
$375$	0	0
$376$	−1.44397e8	−0.140088
$377$	− 1.44734e8i	− 0.139116i
$378$	2.93141e8i	0.279161i
$379$	−6.07726e8	−0.573417	−0.286708	−	0.958018i	$-0.592561\pi$
$379$	−6.07726e8	−0.573417	−0.286708	+	0.958018i	$0.592561\pi$
$380$	0	0
$381$	1.55606e9	1.44141
$382$	9.34467e8i	0.857713i
$383$	1.54124e8i	0.140176i	0.997541	+	0.0700882i	$0.0223281\pi$
$383$	1.54124e8i	0.140176i	−0.997541	+	0.0700882i	$0.977672\pi$
$384$	−9.29041e7	−0.0837289
$385$	0	0
$386$	−1.38011e9	−1.22140
$387$	5.85065e7i	0.0513116i
$388$	− 6.30245e8i	− 0.547770i
$389$	1.99567e9	1.71896	0.859480	−	0.511170i	$-0.170788\pi$
$389$	1.99567e9	1.71896	0.859480	+	0.511170i	$0.170788\pi$
$390$	0	0
$391$	−1.15496e9	−0.977125
$392$	6.02363e7i	0.0505076i
$393$	− 2.12179e9i	− 1.76331i
$394$	9.05968e8	0.746236
$395$	0	0
$396$	−1.19179e8	−0.0964419
$397$	6.91714e8i	0.554830i	0.960750	+	0.277415i	$0.0894777\pi$
$397$	6.91714e8i	0.554830i	−0.960750	+	0.277415i	$0.910522\pi$
$398$	− 1.50395e9i	− 1.19576i
$399$	−3.44825e8	−0.271765
$400$	0	0
$401$	−5.80549e8	−0.449608	−0.224804	−	0.974404i	$-0.572174\pi$
$401$	−5.80549e8	−0.449608	−0.224804	+	0.974404i	$0.572174\pi$
$402$	− 4.74314e7i	− 0.0364145i
$403$	− 1.14048e8i	− 0.0867998i
$404$	−1.21170e9	−0.914242
$405$	0	0
$406$	−1.90325e8	−0.141142
$407$	2.50441e9i	1.84130i
$408$	− 5.05268e8i	− 0.368308i
$409$	1.05158e9	0.759997	0.379998	−	0.924987i	$-0.375925\pi$
$409$	1.05158e9	0.759997	0.379998	+	0.924987i	$0.375925\pi$
$410$	0	0
$411$	−1.42603e8	−0.101317
$412$	− 1.20783e9i	− 0.850871i
$413$	− 3.29860e8i	− 0.230411i
$414$	−9.31170e7	−0.0644953
$415$	0	0
$416$	6.83768e7	0.0465674
$417$	1.29588e9i	0.875164i
$418$	− 1.50588e9i	− 1.00850i
$419$	−1.96750e9	−1.30667	−0.653335	−	0.757069i	$-0.726631\pi$
$419$	−1.96750e9	−1.30667	−0.653335	+	0.757069i	$0.726631\pi$
$420$	0	0
$421$	−2.78313e8	−0.181780	−0.0908901	−	0.995861i	$-0.528971\pi$
$421$	−2.78313e8	−0.181780	−0.0908901	+	0.995861i	$0.528971\pi$
$422$	− 1.63780e8i	− 0.106088i
$423$	− 6.33148e7i	− 0.0406737i
$424$	−2.11492e8	−0.134745
$425$	0	0
$426$	−2.02564e9	−1.26949
$427$	− 8.65431e8i	− 0.537941i
$428$	1.12432e8i	0.0693168i
$429$	−7.66770e8	−0.468883
$430$	0	0
$431$	−2.77969e9	−1.67234	−0.836172	−	0.548467i	$-0.815212\pi$
$431$	−2.77969e9	−1.67234	−0.836172	+	0.548467i	$0.815212\pi$
$432$	− 4.37575e8i	− 0.261131i
$433$	− 1.40755e9i	− 0.833213i	−0.909087	−	0.416607i	$-0.863219\pi$
$433$	− 1.40755e9i	− 0.833213i	0.909087	−	0.416607i	$-0.136781\pi$
$434$	−1.49972e8	−0.0880638
$435$	0	0
$436$	−9.66590e8	−0.558521
$437$	− 1.17658e9i	− 0.674429i
$438$	− 1.01458e7i	− 0.00576935i
$439$	1.57299e9	0.887362	0.443681	−	0.896185i	$-0.353672\pi$
$439$	1.57299e9	0.887362	0.443681	+	0.896185i	$0.353672\pi$
$440$	0	0
$441$	−2.64123e7	−0.0146646
$442$	3.71874e8i	0.204842i
$443$	− 1.33047e9i	− 0.727098i	−0.931575	−	0.363549i	$-0.881565\pi$
$443$	− 1.33047e9i	− 0.727098i	0.931575	−	0.363549i	$-0.118435\pi$
$444$	−8.56031e8	−0.464140
$445$	0	0
$446$	1.56945e9	0.837675
$447$	9.39888e8i	0.497737i
$448$	− 8.99154e7i	− 0.0472456i
$449$	−2.75936e9	−1.43862	−0.719310	−	0.694689i	$-0.755542\pi$
$449$	−2.75936e9	−1.43862	−0.719310	+	0.694689i	$0.755542\pi$
$450$	0	0
$451$	−9.95704e8	−0.511108
$452$	− 5.79558e8i	− 0.295197i
$453$	1.20213e9i	0.607586i
$454$	−7.93691e8	−0.398067
$455$	0	0
$456$	5.14724e8	0.254213
$457$	− 4.55675e8i	− 0.223331i	−0.993746	−	0.111665i	$-0.964381\pi$
$457$	− 4.55675e8i	− 0.223331i	0.993746	−	0.111665i	$-0.0356185\pi$
$458$	− 2.24590e8i	− 0.109235i
$459$	2.37979e9	1.14867
$460$	0	0
$461$	−4.27395e8	−0.203178	−0.101589	−	0.994826i	$-0.532393\pi$
$461$	−4.27395e8	−0.203178	−0.101589	+	0.994826i	$0.532393\pi$
$462$	1.00830e9i	0.475711i
$463$	4.30814e8i	0.201724i	0.994900	+	0.100862i	$0.0321600\pi$
$463$	4.30814e8i	0.201724i	−0.994900	+	0.100862i	$0.967840\pi$
$464$	2.84100e8	0.132026
$465$	0	0
$466$	−2.07797e8	−0.0951236
$467$	− 3.54276e9i	− 1.60966i	−0.593508	−	0.804828i	$-0.702257\pi$
$467$	− 3.54276e9i	− 1.60966i	0.593508	−	0.804828i	$-0.297743\pi$
$468$	2.99817e7i	0.0135206i
$469$	4.59055e7	0.0205476
$470$	0	0
$471$	−6.70086e8	−0.295500
$472$	4.92385e8i	0.215530i
$473$	2.16166e9i	0.939235i
$474$	2.69851e9	1.16386
$475$	0	0
$476$	4.89014e8	0.207825
$477$	− 9.27346e7i	− 0.0391226i
$478$	2.31700e9i	0.970351i
$479$	−2.18067e9	−0.906601	−0.453301	−	0.891358i	$-0.649754\pi$
$479$	−2.18067e9	−0.906601	−0.453301	+	0.891358i	$0.649754\pi$
$480$	0	0
$481$	6.30033e8	0.258140
$482$	− 1.88179e9i	− 0.765432i
$483$	7.87808e8i	0.318131i
$484$	−3.15617e9	−1.26532
$485$	0	0
$486$	3.65871e8	0.144578
$487$	8.94148e8i	0.350799i	0.984497	+	0.175399i	$0.0561217\pi$
$487$	8.94148e8i	0.350799i	−0.984497	+	0.175399i	$0.943878\pi$
$488$	1.29184e9i	0.503198i
$489$	4.47791e9	1.73179
$490$	0	0
$491$	4.17252e9	1.59079	0.795396	−	0.606090i	$-0.207263\pi$
$491$	4.17252e9	1.59079	0.795396	+	0.606090i	$0.207263\pi$
$492$	− 3.40340e8i	− 0.128836i
$493$	1.54511e9i	0.580758i
$494$	−3.78834e8	−0.141385
$495$	0	0
$496$	2.23866e8	0.0823762
$497$	− 1.96048e9i	− 0.716332i
$498$	9.38605e8i	0.340550i
$499$	−8.93170e8	−0.321797	−0.160899	−	0.986971i	$-0.551439\pi$
$499$	−8.93170e8	−0.321797	−0.160899	+	0.986971i	$0.551439\pi$
$500$	0	0
$501$	−2.14296e9	−0.761346
$502$	2.96853e9i	1.04732i
$503$	2.88740e9i	1.01162i	0.862644	+	0.505812i	$0.168807\pi$
$503$	2.88740e9i	1.01162i	−0.862644	+	0.505812i	$0.831193\pi$
$504$	3.94259e7	0.0137175
$505$	0	0
$506$	−3.44043e9	−1.18056
$507$	− 2.58687e9i	− 0.881550i
$508$	− 2.24802e9i	− 0.760813i
$509$	1.04446e9	0.351059	0.175529	−	0.984474i	$-0.443836\pi$
$509$	1.04446e9	0.351059	0.175529	+	0.984474i	$0.443836\pi$
$510$	0	0
$511$	9.81942e6	0.00325546
$512$	1.34218e8i	0.0441942i
$513$	2.42433e9i	0.792832i
$514$	−2.02805e9	−0.658730
$515$	0	0
$516$	−7.38876e8	−0.236754
$517$	− 2.33932e9i	− 0.744513i
$518$	− 8.28493e8i	− 0.261899i
$519$	−2.66815e8	−0.0837769
$520$	0	0
$521$	1.58851e9	0.492106	0.246053	−	0.969256i	$-0.420866\pi$
$521$	1.58851e9	0.492106	0.246053	+	0.969256i	$0.420866\pi$
$522$	1.24572e8i	0.0383330i
$523$	4.73420e9i	1.44707i	0.690286	+	0.723537i	$0.257485\pi$
$523$	4.73420e9i	1.44707i	−0.690286	+	0.723537i	$0.742515\pi$
$524$	−3.06533e9	−0.930717
$525$	0	0
$526$	2.71593e9	0.813709
$527$	1.21752e9i	0.362358i
$528$	− 1.50510e9i	− 0.444987i
$529$	7.16738e8	0.210507
$530$	0	0
$531$	−2.15900e8	−0.0625780
$532$	4.98166e8i	0.143444i
$533$	2.50488e8i	0.0716543i
$534$	2.77444e9	0.788464
$535$	0	0
$536$	−6.85237e7	−0.0192205
$537$	− 4.63056e8i	− 0.129040i
$538$	− 1.21427e9i	− 0.336184i
$539$	−9.75865e8	−0.268429
$540$	0	0
$541$	4.26233e9	1.15733	0.578665	−	0.815566i	$-0.303574\pi$
$541$	4.26233e9	1.15733	0.578665	+	0.815566i	$0.303574\pi$
$542$	4.87688e8i	0.131566i
$543$	− 4.51019e9i	− 1.20891i
$544$	−7.29957e8	−0.194402
$545$	0	0
$546$	2.53658e8	0.0666920
$547$	− 5.20549e9i	− 1.35990i	−0.733260	−	0.679948i	$-0.762002\pi$
$547$	− 5.20549e9i	− 1.35990i	0.733260	−	0.679948i	$-0.237998\pi$
$548$	2.06018e8i	0.0534777i
$549$	−5.66442e8	−0.146101
$550$	0	0
$551$	−1.57402e9	−0.400849
$552$	− 1.17597e9i	− 0.297584i
$553$	2.61170e9i	0.656727i
$554$	1.82213e9	0.455298
$555$	0	0
$556$	1.87215e9	0.461933
$557$	− 1.04344e9i	− 0.255844i	−0.991784	−	0.127922i	$-0.959169\pi$
$557$	− 1.04344e9i	− 0.255844i	0.991784	−	0.127922i	$-0.0408307\pi$
$558$	9.81601e7i	0.0239175i
$559$	5.43808e8	0.131675
$560$	0	0
$561$	8.18565e9	1.95742
$562$	3.89531e9i	0.925688i
$563$	− 8.23842e9i	− 1.94565i	−0.231541	−	0.972825i	$-0.574377\pi$
$563$	− 8.23842e9i	− 1.94565i	0.231541	−	0.972825i	$-0.425623\pi$
$564$	7.99599e8	0.187670
$565$	0	0
$566$	−2.09748e9	−0.486228
$567$	− 1.45486e9i	− 0.335183i
$568$	2.92643e9i	0.670068i
$569$	−6.17425e9	−1.40505	−0.702525	−	0.711659i	$-0.747944\pi$
$569$	−6.17425e9	−1.40505	−0.702525	+	0.711659i	$0.747944\pi$
$570$	0	0
$571$	4.44117e9	0.998324	0.499162	−	0.866509i	$-0.333641\pi$
$571$	4.44117e9	0.998324	0.499162	+	0.866509i	$0.333641\pi$
$572$	1.10775e9i	0.247488i
$573$	− 5.17462e9i	− 1.14905i
$574$	3.29392e8	0.0726978
$575$	0	0
$576$	−5.88515e7	−0.0128315
$577$	8.17132e9i	1.77083i	0.464801	+	0.885415i	$0.346126\pi$
$577$	8.17132e9i	1.77083i	−0.464801	+	0.885415i	$0.653874\pi$
$578$	− 6.87233e8i	− 0.148032i
$579$	7.64238e9	1.63626
$580$	0	0
$581$	−9.08411e8	−0.192161
$582$	3.48999e9i	0.733827i
$583$	− 3.42630e9i	− 0.716120i
$584$	−1.46576e7	−0.00304521
$585$	0	0
$586$	5.94263e8	0.121994
$587$	− 6.28754e9i	− 1.28306i	−0.767097	−	0.641531i	$-0.778300\pi$
$587$	− 6.28754e9i	− 1.28306i	0.767097	−	0.641531i	$-0.221700\pi$
$588$	− 3.33559e8i	− 0.0676632i
$589$	−1.24030e9	−0.250106
$590$	0	0
$591$	−5.01681e9	−0.999704
$592$	1.23670e9i	0.244984i
$593$	7.01629e9i	1.38171i	0.722995	+	0.690854i	$0.242765\pi$
$593$	7.01629e9i	1.38171i	−0.722995	+	0.690854i	$0.757235\pi$
$594$	7.08898e9	1.38781
$595$	0	0
$596$	1.35785e9	0.262718
$597$	8.32816e9i	1.60191i
$598$	8.65507e8i	0.165507i
$599$	9.38103e8	0.178343	0.0891716	−	0.996016i	$-0.471578\pi$
$599$	9.38103e8	0.178343	0.0891716	+	0.996016i	$0.471578\pi$
$600$	0	0
$601$	2.95585e9	0.555421	0.277711	−	0.960665i	$-0.410424\pi$
$601$	2.95585e9	0.555421	0.277711	+	0.960665i	$0.410424\pi$
$602$	− 7.15107e8i	− 0.133593i
$603$	− 3.00461e7i	− 0.00558056i
$604$	1.73671e9	0.320699
$605$	0	0
$606$	6.70982e9	1.22478
$607$	− 4.76325e9i	− 0.864457i	−0.901764	−	0.432228i	$-0.857727\pi$
$607$	− 4.76325e9i	− 0.864457i	0.901764	−	0.432228i	$-0.142273\pi$
$608$	− 7.43617e8i	− 0.134180i
$609$	1.05393e9	0.189082
$610$	0	0
$611$	−5.88500e8	−0.104376
$612$	− 3.20070e8i	− 0.0564436i
$613$	2.32881e9i	0.408340i	0.978935	+	0.204170i	$0.0654495\pi$
$613$	2.32881e9i	0.408340i	−0.978935	+	0.204170i	$0.934550\pi$
$614$	3.71673e9	0.647996
$615$	0	0
$616$	1.45668e9	0.251092
$617$	9.82915e9i	1.68468i	0.538945	+	0.842341i	$0.318823\pi$
$617$	9.82915e9i	1.68468i	−0.538945	+	0.842341i	$0.681177\pi$
$618$	6.68835e9i	1.13988i
$619$	5.94350e8	0.100722	0.0503611	−	0.998731i	$-0.483963\pi$
$619$	5.94350e8	0.100722	0.0503611	+	0.998731i	$0.483963\pi$
$620$	0	0
$621$	5.53878e9	0.928097
$622$	− 5.47801e9i	− 0.912760i
$623$	2.68519e9i	0.444905i
$624$	−3.78637e8	−0.0623846
$625$	0	0
$626$	−2.28763e9	−0.372713
$627$	8.33884e9i	1.35104i
$628$	9.68068e8i	0.155972i
$629$	−6.72592e9	−1.07764
$630$	0	0
$631$	6.06380e9	0.960820	0.480410	−	0.877044i	$-0.340488\pi$
$631$	6.06380e9	0.960820	0.480410	+	0.877044i	$0.340488\pi$
$632$	− 3.89851e9i	− 0.614312i
$633$	9.06931e8i	0.142122i
$634$	−6.54354e9	−1.01977
$635$	0	0
$636$	1.17114e9	0.180513
$637$	2.45498e8i	0.0376322i
$638$	4.60260e9i	0.701667i
$639$	−1.28317e9	−0.194550
$640$	0	0
$641$	−7.74978e8	−0.116221	−0.0581107	−	0.998310i	$-0.518508\pi$
$641$	−7.74978e8	−0.116221	−0.0581107	+	0.998310i	$0.518508\pi$
$642$	− 6.22596e8i	− 0.0928611i
$643$	1.39116e9i	0.206366i	0.994662	+	0.103183i	$0.0329028\pi$
$643$	1.39116e9i	0.206366i	−0.994662	+	0.103183i	$0.967097\pi$
$644$	1.13814e9	0.167917
$645$	0	0
$646$	4.04424e9	0.590232
$647$	8.16793e9i	1.18562i	0.805341	+	0.592812i	$0.201982\pi$
$647$	8.16793e9i	1.18562i	−0.805341	+	0.592812i	$0.798018\pi$
$648$	2.17169e9i	0.313535i
$649$	−7.97694e9	−1.14546
$650$	0	0
$651$	8.30475e8	0.117976
$652$	− 6.46920e9i	− 0.914079i
$653$	3.75842e9i	0.528213i	0.964493	+	0.264107i	$0.0850771\pi$
$653$	3.75842e9i	0.528213i	−0.964493	+	0.264107i	$0.914923\pi$
$654$	5.35250e9	0.748230
$655$	0	0
$656$	−4.91687e8	−0.0680026
$657$	− 6.42701e6i	0 0.000884159i
$658$	7.73877e8i	0.105896i
$659$	1.11612e10	1.51919	0.759594	−	0.650398i	$-0.225398\pi$
$659$	1.11612e10	1.51919	0.759594	+	0.650398i	$0.225398\pi$
$660$	0	0
$661$	−7.25634e8	−0.0977265	−0.0488632	−	0.998805i	$-0.515560\pi$
$661$	−7.25634e8	−0.0977265	−0.0488632	+	0.998805i	$0.515560\pi$
$662$	7.57658e9i	1.01501i
$663$	− 2.05926e9i	− 0.274419i
$664$	1.35600e9	0.179750
$665$	0	0
$666$	−5.42266e8	−0.0711299
$667$	3.59612e9i	0.469238i
$668$	3.09592e9i	0.401857i
$669$	−8.69086e9	−1.12220
$670$	0	0
$671$	−2.09286e10	−2.67431
$672$	4.97908e8i	0.0632931i
$673$	− 3.86734e9i	− 0.489057i	−0.969642	−	0.244528i	$-0.921367\pi$
$673$	− 3.86734e9i	− 0.489057i	0.969642	−	0.244528i	$-0.0786331\pi$
$674$	1.09228e10	1.37412
$675$	0	0
$676$	−3.73723e9	−0.465304
$677$	6.50913e9i	0.806237i	0.915148	+	0.403118i	$0.132074\pi$
$677$	6.50913e9i	0.806237i	−0.915148	+	0.403118i	$0.867926\pi$
$678$	3.20931e9i	0.395465i
$679$	−3.37772e9	−0.414076
$680$	0	0
$681$	4.39507e9	0.533275
$682$	3.62676e9i	0.437798i
$683$	5.96614e9i	0.716508i	0.933624	+	0.358254i	$0.116628\pi$
$683$	5.96614e9i	0.716508i	−0.933624	+	0.358254i	$0.883372\pi$
$684$	3.26060e8	0.0389584
$685$	0	0
$686$	3.22829e8	0.0381802
$687$	1.24367e9i	0.146338i
$688$	1.06745e9i	0.124965i
$689$	−8.61953e8	−0.100396
$690$	0	0
$691$	4.47683e9	0.516176	0.258088	−	0.966121i	$-0.416908\pi$
$691$	4.47683e9	0.516176	0.258088	+	0.966121i	$0.416908\pi$
$692$	3.85465e8i	0.0442195i
$693$	6.38724e8i	0.0729032i
$694$	−7.73081e9	−0.877944
$695$	0	0
$696$	−1.57321e9	−0.176870
$697$	− 2.67409e9i	− 0.299131i
$698$	− 5.20706e9i	− 0.579560i
$699$	1.15068e9	0.127434
$700$	0	0
$701$	−5.17249e9	−0.567135	−0.283568	−	0.958952i	$-0.591518\pi$
$701$	−5.17249e9	−0.567135	−0.283568	+	0.958952i	$0.591518\pi$
$702$	− 1.78337e9i	− 0.194563i
$703$	− 6.85179e9i	− 0.743808i
$704$	−2.17441e9	−0.234875
$705$	0	0
$706$	4.83069e9	0.516645
$707$	6.49397e9i	0.691102i
$708$	− 2.72659e9i	− 0.288738i
$709$	1.92689e8	0.0203046	0.0101523	−	0.999948i	$-0.496768\pi$
$709$	1.92689e8	0.0203046	0.0101523	+	0.999948i	$0.496768\pi$
$710$	0	0
$711$	1.70941e9	0.178362
$712$	− 4.00822e9i	− 0.416171i
$713$	2.83367e9i	0.292776i
$714$	−2.70792e9	−0.278415
$715$	0	0
$716$	−6.68973e8	−0.0681103
$717$	− 1.28304e10i	− 1.29994i
$718$	− 6.85523e8i	− 0.0691173i
$719$	9.94078e8	0.0997400	0.0498700	−	0.998756i	$-0.484119\pi$
$719$	9.94078e8	0.0997400	0.0498700	+	0.998756i	$0.484119\pi$
$720$	0	0
$721$	−6.47319e9	−0.643198
$722$	− 3.03105e9i	− 0.299718i
$723$	1.04204e10i	1.02542i
$724$	−6.51584e9	−0.638095
$725$	0	0
$726$	1.74773e10	1.69510
$727$	− 2.06212e8i	− 0.0199042i	−0.999950	−	0.00995208i	$-0.996832\pi$
$727$	− 2.06212e8i	− 0.0199042i	0.999950	−	0.00995208i	$-0.00316790\pi$
$728$	− 3.66457e8i	− 0.0352017i
$729$	−1.13024e10	−1.08050
$730$	0	0
$731$	−5.80542e9	−0.549697
$732$	− 7.15358e9i	− 0.674116i
$733$	8.04851e9i	0.754834i	0.926043	+	0.377417i	$0.123188\pi$
$733$	8.04851e9i	0.754834i	−0.926043	+	0.377417i	$0.876812\pi$
$734$	1.30927e10	1.22206
$735$	0	0
$736$	−1.69891e9	−0.157072
$737$	− 1.11013e9i	− 0.102149i
$738$	− 2.15594e8i	− 0.0197442i
$739$	5.35129e9	0.487756	0.243878	−	0.969806i	$-0.421580\pi$
$739$	5.35129e9	0.487756	0.243878	+	0.969806i	$0.421580\pi$
$740$	0	0
$741$	2.09780e9	0.189409
$742$	1.13347e9i	0.101858i
$743$	1.53558e10i	1.37345i	0.726919	+	0.686723i	$0.240952\pi$
$743$	1.53558e10i	1.37345i	−0.726919	+	0.686723i	$0.759048\pi$
$744$	−1.23966e9	−0.110356
$745$	0	0
$746$	−1.50444e10	−1.32675
$747$	5.94574e8i	0.0521896i
$748$	− 1.18257e10i	− 1.03317i
$749$	6.02568e8	0.0523986
$750$	0	0
$751$	2.05007e9	0.176615	0.0883077	−	0.996093i	$-0.471854\pi$
$751$	2.05007e9	0.176615	0.0883077	+	0.996093i	$0.471854\pi$
$752$	− 1.15517e9i	− 0.0990570i
$753$	− 1.64383e10i	− 1.40305i
$754$	1.15787e9	0.0983697
$755$	0	0
$756$	−2.34513e9	−0.197397
$757$	− 1.05302e10i	− 0.882270i	−0.897441	−	0.441135i	$-0.854576\pi$
$757$	− 1.05302e10i	− 0.882270i	0.897441	−	0.441135i	$-0.145424\pi$
$758$	− 4.86181e9i	− 0.405467i
$759$	1.90514e10	1.58155
$760$	0	0
$761$	1.69743e10	1.39620	0.698098	−	0.716002i	$-0.254030\pi$
$761$	1.69743e10	1.39620	0.698098	+	0.716002i	$0.254030\pi$
$762$	1.24485e10i	1.01923i
$763$	5.18032e9i	0.422202i
$764$	−7.47573e9	−0.606495
$765$	0	0
$766$	−1.23299e9	−0.0991198
$767$	2.00675e9i	0.160587i
$768$	− 7.43232e8i	− 0.0592053i
$769$	−3.02600e9	−0.239953	−0.119977	−	0.992777i	$-0.538282\pi$
$769$	−3.02600e9	−0.239953	−0.119977	+	0.992777i	$0.538282\pi$
$770$	0	0
$771$	1.12303e10	0.882476
$772$	− 1.10409e10i	− 0.863661i
$773$	1.38384e10i	1.07760i	0.842434	+	0.538799i	$0.181122\pi$
$773$	1.38384e10i	1.07760i	−0.842434	+	0.538799i	$0.818878\pi$
$774$	−4.68052e8	−0.0362828
$775$	0	0
$776$	5.04196e9	0.387332
$777$	4.58779e9i	0.350857i
$778$	1.59654e10i	1.21549i
$779$	2.72413e9	0.206465
$780$	0	0
$781$	−4.74099e10	−3.56115
$782$	− 9.23972e9i	− 0.690932i
$783$	− 7.40976e9i	− 0.551617i
$784$	−4.81890e8	−0.0357143
$785$	0	0
$786$	1.69743e10	1.24685
$787$	− 9.83270e9i	− 0.719054i	−0.933135	−	0.359527i	$-0.882938\pi$
$787$	− 9.83270e9i	− 0.719054i	0.933135	−	0.359527i	$-0.117062\pi$
$788$	7.24775e9i	0.527669i
$789$	−1.50395e10	−1.09009
$790$	0	0
$791$	−3.10607e9	−0.223148
$792$	− 9.53430e8i	− 0.0681947i
$793$	5.26499e9i	0.374922i
$794$	−5.53371e9	−0.392324
$795$	0	0
$796$	1.20316e10	0.845529
$797$	3.16521e9i	0.221462i	0.993850	+	0.110731i	$0.0353191\pi$
$797$	3.16521e9i	0.221462i	−0.993850	+	0.110731i	$0.964681\pi$
$798$	− 2.75860e9i	− 0.192167i
$799$	6.28253e9	0.435733
$800$	0	0
$801$	1.75751e9	0.120833
$802$	− 4.64439e9i	− 0.317921i
$803$	− 2.37461e8i	− 0.0161841i
$804$	3.79451e8	0.0257489
$805$	0	0
$806$	9.12381e8	0.0613767
$807$	6.72403e9i	0.450373i
$808$	− 9.69362e9i	− 0.646467i
$809$	−2.18461e10	−1.45062	−0.725311	−	0.688422i	$-0.758304\pi$
$809$	−2.18461e10	−1.45062	−0.725311	+	0.688422i	$0.758304\pi$
$810$	0	0
$811$	1.11360e10	0.733090	0.366545	−	0.930400i	$-0.380541\pi$
$811$	1.11360e10	0.733090	0.366545	+	0.930400i	$0.380541\pi$
$812$	− 1.52260e9i	− 0.0998022i
$813$	− 2.70058e9i	− 0.176254i
$814$	−2.00353e10	−1.30200
$815$	0	0
$816$	4.04214e9	0.260433
$817$	− 5.91407e9i	− 0.379410i
$818$	8.41266e9i	0.537399i
$819$	1.60683e8	0.0102206
$820$	0	0
$821$	2.08012e9	0.131186	0.0655931	−	0.997846i	$-0.479106\pi$
$821$	2.08012e9	0.131186	0.0655931	+	0.997846i	$0.479106\pi$
$822$	− 1.14083e9i	− 0.0716421i
$823$	− 1.89553e10i	− 1.18531i	−0.805458	−	0.592653i	$-0.798081\pi$
$823$	− 1.89553e10i	− 1.18531i	0.805458	−	0.592653i	$-0.201919\pi$
$824$	9.66260e9	0.601657
$825$	0	0
$826$	2.63888e9	0.162925
$827$	2.12105e10i	1.30401i	0.758215	+	0.652005i	$0.226072\pi$
$827$	2.12105e10i	1.30401i	−0.758215	+	0.652005i	$0.773928\pi$
$828$	− 7.44936e8i	− 0.0456050i
$829$	1.14471e10	0.697840	0.348920	−	0.937152i	$-0.386548\pi$
$829$	1.14471e10	0.697840	0.348920	+	0.937152i	$0.386548\pi$
$830$	0	0
$831$	−1.00901e10	−0.609945
$832$	5.47014e8i	0.0329281i
$833$	− 2.62081e9i	− 0.157101i
$834$	−1.03671e10	−0.618834
$835$	0	0
$836$	1.20471e10	0.713114
$837$	− 5.83875e9i	− 0.344176i
$838$	− 1.57400e10i	− 0.923956i
$839$	−3.31864e10	−1.93996	−0.969981	−	0.243179i	$-0.921810\pi$
$839$	−3.31864e10	−1.93996	−0.969981	+	0.243179i	$0.921810\pi$
$840$	0	0
$841$	−1.24390e10	−0.721107
$842$	− 2.22651e9i	− 0.128538i
$843$	− 2.15703e10i	− 1.24011i
$844$	1.31024e9	0.0750155
$845$	0	0
$846$	5.06518e8	0.0287606
$847$	1.69151e10i	0.956494i
$848$	− 1.69194e9i	− 0.0952794i
$849$	1.16148e10	0.651382
$850$	0	0
$851$	−1.56540e10	−0.870709
$852$	− 1.62051e10i	− 0.897664i
$853$	− 2.28601e10i	− 1.26112i	−0.776140	−	0.630560i	$-0.782825\pi$
$853$	− 2.28601e10i	− 1.26112i	0.776140	−	0.630560i	$-0.217175\pi$
$854$	6.92345e9	0.380382
$855$	0	0
$856$	−8.99460e8	−0.0490144
$857$	2.93946e10i	1.59527i	0.603140	+	0.797635i	$0.293916\pi$
$857$	2.93946e10i	1.59527i	−0.603140	+	0.797635i	$0.706084\pi$
$858$	− 6.13416e9i	− 0.331550i
$859$	−1.12866e10	−0.607558	−0.303779	−	0.952743i	$-0.598248\pi$
$859$	−1.12866e10	−0.607558	−0.303779	+	0.952743i	$0.598248\pi$
$860$	0	0
$861$	−1.82401e9	−0.0973905
$862$	− 2.22375e10i	− 1.18253i
$863$	− 2.36165e10i	− 1.25077i	−0.780315	−	0.625387i	$-0.784941\pi$
$863$	− 2.36165e10i	− 1.25077i	0.780315	−	0.625387i	$-0.215059\pi$
$864$	3.50060e9	0.184648
$865$	0	0
$866$	1.12604e10	0.589171
$867$	3.80556e9i	0.198313i
$868$	− 1.19978e9i	− 0.0622705i
$869$	6.31583e10	3.26483
$870$	0	0
$871$	−2.79274e8	−0.0143208
$872$	− 7.73272e9i	− 0.394934i
$873$	2.21079e9i	0.112460i
$874$	9.41264e9	0.476893
$875$	0	0
$876$	8.11664e7	0.00407955
$877$	− 3.02456e9i	− 0.151413i	−0.997130	−	0.0757065i	$-0.975879\pi$
$877$	− 3.02456e9i	− 0.151413i	0.997130	−	0.0757065i	$-0.0241212\pi$
$878$	1.25839e10i	0.627459i
$879$	−3.29074e9	−0.163430
$880$	0	0
$881$	−2.09728e10	−1.03333	−0.516666	−	0.856187i	$-0.672827\pi$
$881$	−2.09728e10	−1.03333	−0.516666	+	0.856187i	$0.672827\pi$
$882$	− 2.11298e8i	− 0.0103694i
$883$	1.76578e10i	0.863124i	0.902083	+	0.431562i	$0.142037\pi$
$883$	1.76578e10i	0.863124i	−0.902083	+	0.431562i	$0.857963\pi$
$884$	−2.97499e9	−0.144845
$885$	0	0
$886$	1.06438e10	0.514136
$887$	− 3.58732e10i	− 1.72599i	−0.505215	−	0.862993i	$-0.668587\pi$
$887$	− 3.58732e10i	− 1.72599i	0.505215	−	0.862993i	$-0.331413\pi$
$888$	− 6.84825e9i	− 0.328197i
$889$	−1.20480e10	−0.575121
$890$	0	0
$891$	−3.51827e10	−1.66632
$892$	1.25556e10i	0.592326i
$893$	6.40011e9i	0.300751i
$894$	−7.51911e9	−0.351953
$895$	0	0
$896$	7.19323e8	0.0334077
$897$	− 4.79276e9i	− 0.221724i
$898$	− 2.20749e10i	− 1.01726i
$899$	3.79087e9	0.174013
$900$	0	0
$901$	9.20177e9	0.419117
$902$	− 7.96563e9i	− 0.361408i
$903$	3.95991e9i	0.178969i
$904$	4.63646e9	0.208736
$905$	0	0
$906$	−9.61704e9	−0.429628
$907$	− 1.65563e10i	− 0.736780i	−0.929671	−	0.368390i	$-0.879909\pi$
$907$	− 1.65563e10i	− 0.736780i	0.929671	−	0.368390i	$-0.120091\pi$
$908$	− 6.34953e9i	− 0.281476i
$909$	4.25044e9	0.187698
$910$	0	0
$911$	2.04661e9	0.0896852	0.0448426	−	0.998994i	$-0.485721\pi$
$911$	2.04661e9	0.0896852	0.0448426	+	0.998994i	$0.485721\pi$
$912$	4.11779e9i	0.179756i
$913$	2.19680e10i	0.955305i
$914$	3.64540e9	0.157919
$915$	0	0
$916$	1.79672e9	0.0772407
$917$	1.64283e10i	0.703556i
$918$	1.90383e10i	0.812232i
$919$	−3.62621e10	−1.54116	−0.770582	−	0.637341i	$-0.780034\pi$
$919$	−3.62621e10	−1.54116	−0.770582	+	0.637341i	$0.780034\pi$
$920$	0	0
$921$	−2.05815e10	−0.868096
$922$	− 3.41916e9i	− 0.143669i
$923$	1.19269e10i	0.499253i
$924$	−8.06641e9	−0.336379
$925$	0	0
$926$	−3.44652e9	−0.142640
$927$	4.23683e9i	0.174688i
$928$	2.27280e9i	0.0933564i
$929$	1.05595e10	0.432105	0.216053	−	0.976382i	$-0.430682\pi$
$929$	1.05595e10	0.432105	0.216053	+	0.976382i	$0.430682\pi$
$930$	0	0
$931$	2.66986e9	0.108434
$932$	− 1.66238e9i	− 0.0672626i
$933$	3.03346e10i	1.22279i
$934$	2.83421e10	1.13820
$935$	0	0
$936$	−2.39854e8	−0.00956050
$937$	− 5.66531e9i	− 0.224975i	−0.993653	−	0.112488i	$-0.964118\pi$
$937$	− 5.66531e9i	− 0.224975i	0.993653	−	0.112488i	$-0.0358819\pi$
$938$	3.67244e8i	0.0145293i
$939$	1.26678e10	0.499310
$940$	0	0
$941$	−3.76376e10	−1.47251	−0.736255	−	0.676704i	$-0.763408\pi$
$941$	−3.76376e10	−1.47251	−0.736255	+	0.676704i	$0.763408\pi$
$942$	− 5.36069e9i	− 0.208950i
$943$	− 6.22373e9i	− 0.241690i
$944$	−3.93908e9	−0.152403
$945$	0	0
$946$	−1.72933e10	−0.664139
$947$	3.56031e10i	1.36227i	0.732159	+	0.681134i	$0.238513\pi$
$947$	3.56031e10i	1.36227i	−0.732159	+	0.681134i	$0.761487\pi$
$948$	2.15881e10i	0.822970i
$949$	−5.97380e7	−0.00226892
$950$	0	0
$951$	3.62350e10	1.36614
$952$	3.91211e9i	0.146954i
$953$	− 3.27959e10i	− 1.22742i	−0.789530	−	0.613712i	$-0.789675\pi$
$953$	− 3.27959e10i	− 1.22742i	0.789530	−	0.613712i	$-0.210325\pi$
$954$	7.41877e8	0.0276638
$955$	0	0
$956$	−1.85360e10	−0.686142
$957$	− 2.54870e10i	− 0.939997i
$958$	− 1.74454e10i	− 0.641064i
$959$	1.10413e9	0.0404253
$960$	0	0
$961$	−2.45255e10	−0.891427
$962$	5.04027e9i	0.182533i
$963$	− 3.94393e8i	− 0.0142311i
$964$	1.50543e10	0.541242
$965$	0	0
$966$	−6.30247e9	−0.224952
$967$	− 1.21805e10i	− 0.433184i	−0.976262	−	0.216592i	$-0.930506\pi$
$967$	− 1.21805e10i	− 0.433184i	0.976262	−	0.216592i	$-0.0694941\pi$
$968$	− 2.52493e10i	− 0.894718i
$969$	−2.23950e10	−0.790712
$970$	0	0
$971$	2.37312e10	0.831865	0.415933	−	0.909395i	$-0.363455\pi$
$971$	2.37312e10	0.831865	0.415933	+	0.909395i	$0.363455\pi$
$972$	2.92697e9i	0.102232i
$973$	− 1.00336e10i	− 0.349188i
$974$	−7.15318e9	−0.248052
$975$	0	0
$976$	−1.03347e10	−0.355815
$977$	3.44206e9i	0.118083i	0.998256	+	0.0590416i	$0.0188044\pi$
$977$	3.44206e9i	0.118083i	−0.998256	+	0.0590416i	$0.981196\pi$
$978$	3.58233e10i	1.22456i
$979$	6.49356e10	2.21179
$980$	0	0
$981$	3.39062e9	0.114667
$982$	3.33802e10i	1.12486i
$983$	− 5.25354e10i	− 1.76407i	−0.471187	−	0.882033i	$-0.656174\pi$
$983$	− 5.25354e10i	− 1.76407i	0.471187	−	0.882033i	$-0.343826\pi$
$984$	2.72272e9	0.0911005
$985$	0	0
$986$	−1.23609e10	−0.410658
$987$	− 4.28535e9i	− 0.141865i
$988$	− 3.03067e9i	− 0.0999745i
$989$	−1.35117e10	−0.444142
$990$	0	0
$991$	5.03399e10	1.64306	0.821531	−	0.570163i	$-0.193120\pi$
$991$	5.03399e10	1.64306	0.821531	+	0.570163i	$0.193120\pi$
$992$	1.79092e9i	0.0582487i
$993$	− 4.19554e10i	− 1.35977i
$994$	1.56838e10	0.506524
$995$	0	0
$996$	−7.50884e9	−0.240805
$997$	− 4.80693e9i	− 0.153615i	−0.997046	−	0.0768077i	$-0.975527\pi$
$997$	− 4.80693e9i	− 0.153615i	0.997046	−	0.0768077i	$-0.0244727\pi$
$998$	− 7.14536e9i	− 0.227545i
$999$	3.22550e10	1.02357

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.8.c.i.99.3		4
5.2	odd	4		350.8.a.l.1.1		2
5.3	odd	4		70.8.a.g.1.2	✓	2
5.4	even	2	inner	350.8.c.i.99.2		4
20.3	even	4		560.8.a.h.1.1		2
35.13	even	4		490.8.a.k.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.8.a.g.1.2	✓	2	5.3	odd	4
350.8.a.l.1.1		2	5.2	odd	4
350.8.c.i.99.2		4	5.4	even	2	inner
350.8.c.i.99.3		4	1.1	even	1	trivial
490.8.a.k.1.1		2	35.13	even	4
560.8.a.h.1.1		2	20.3	even	4

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	350.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+8.00000i q^{2} -44.3001i q^{3} -64.0000 q^{4} +354.401 q^{6} +343.000i q^{7} -512.000i q^{8} +224.501 q^{9} +O(q^{10})\)	\(q+8.00000i q^{2} -44.3001i q^{3} -64.0000 q^{4} +354.401 q^{6} +343.000i q^{7} -512.000i q^{8} +224.501 q^{9} +8294.71 q^{11} +2835.21i q^{12} -2086.69i q^{13} -2744.00 q^{14} +4096.00 q^{16} +22276.5i q^{17} +1796.00i q^{18} -22693.4 q^{19} +15194.9 q^{21} +66357.7i q^{22} +51846.8i q^{23} -22681.7 q^{24} +16693.6 q^{26} -106830. i q^{27} -21952.0i q^{28} +69360.5 q^{29} +54654.7 q^{31} +32768.0i q^{32} -367457. i q^{33} -178212. q^{34} -14368.0 q^{36} +301929. i q^{37} -181547. i q^{38} -92440.8 q^{39} -120041. q^{41} +121559. i q^{42} +260607. i q^{43} -530862. q^{44} -414774. q^{46} -282025. i q^{47} -181453. i q^{48} -117649. q^{49} +986852. q^{51} +133548. i q^{52} -413071. i q^{53} +854638. q^{54} +175616. q^{56} +1.00532e6i q^{57} +554884. i q^{58} -961690. q^{59} -2.52312e6 q^{61} +437238. i q^{62} +77003.7i q^{63} -262144. q^{64} +2.93965e6 q^{66} -133835. i q^{67} -1.42570e6i q^{68} +2.29682e6 q^{69} -5.71568e6 q^{71} -114944. i q^{72} -28628.0i q^{73} -2.41543e6 q^{74} +1.45238e6 q^{76} +2.84509e6i q^{77} -739526. i q^{78} +7.61428e6 q^{79} -4.24159e6 q^{81} -960326. i q^{82} +2.64843e6i q^{83} -972476. q^{84} -2.08486e6 q^{86} -3.07268e6i q^{87} -4.24689e6i q^{88} +7.82855e6 q^{89} +715736. q^{91} -3.31819e6i q^{92} -2.42121e6i q^{93} +2.25620e6 q^{94} +1.45163e6 q^{96} +9.84758e6i q^{97} -941192. i q^{98} +1.86217e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 256 q^{4} - 80 q^{6} - 38 q^{9}+O(q^{10}) \) 4 * q - 256 * q^4 - 80 * q^6 - 38 * q^9	\( 4 q - 256 q^{4} - 80 q^{6} - 38 q^{9} + 9030 q^{11} - 10976 q^{14} + 16384 q^{16} - 87404 q^{19} - 3430 q^{21} + 5120 q^{24} + 143152 q^{26} - 18522 q^{29} + 414056 q^{31} - 600528 q^{34} + 2432 q^{36} + 491546 q^{39} + 529596 q^{41} - 577920 q^{44} + 650208 q^{46} - 470596 q^{49} + 469410 q^{51} + 176240 q^{54} + 702464 q^{56} - 3810816 q^{59} - 238636 q^{61} - 1048576 q^{64} + 8860752 q^{66} + 13712652 q^{69} - 1225344 q^{71} + 2289152 q^{74} + 5593856 q^{76} + 25241518 q^{79} - 18995596 q^{81} + 219520 q^{84} - 8402336 q^{86} + 22356660 q^{89} + 6137642 q^{91} + 8121744 q^{94} - 327680 q^{96} + 5565060 q^{99}+O(q^{100}) \) 4 * q - 256 * q^4 - 80 * q^6 - 38 * q^9 + 9030 * q^11 - 10976 * q^14 + 16384 * q^16 - 87404 * q^19 - 3430 * q^21 + 5120 * q^24 + 143152 * q^26 - 18522 * q^29 + 414056 * q^31 - 600528 * q^34 + 2432 * q^36 + 491546 * q^39 + 529596 * q^41 - 577920 * q^44 + 650208 * q^46 - 470596 * q^49 + 469410 * q^51 + 176240 * q^54 + 702464 * q^56 - 3810816 * q^59 - 238636 * q^61 - 1048576 * q^64 + 8860752 * q^66 + 13712652 * q^69 - 1225344 * q^71 + 2289152 * q^74 + 5593856 * q^76 + 25241518 * q^79 - 18995596 * q^81 + 219520 * q^84 - 8402336 * q^86 + 22356660 * q^89 + 6137642 * q^91 + 8121744 * q^94 - 327680 * q^96 + 5565060 * q^99

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