# Properties

 Label 1305.2.c.b.784.2 Level $1305$ Weight $2$ Character 1305.784 Analytic conductor $10.420$ Analytic rank $0$ Dimension $2$ Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1305,2,Mod(784,1305)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1305, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1305.784");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1305 = 3^{2} \cdot 5 \cdot 29$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1305.c (of order $$2$$, degree $$1$$, 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: $$10.4204774638$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} + 1$$ x^2 + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 435) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 784.2 Root $$1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1305.784 Dual form 1305.2.c.b.784.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+1.00000i q^{2} +1.00000 q^{4} +(-1.00000 - 2.00000i) q^{5} +2.00000i q^{7} +3.00000i q^{8} +O(q^{10})$$ $$q+1.00000i q^{2} +1.00000 q^{4} +(-1.00000 - 2.00000i) q^{5} +2.00000i q^{7} +3.00000i q^{8} +(2.00000 - 1.00000i) q^{10} +4.00000i q^{13} -2.00000 q^{14} -1.00000 q^{16} +2.00000i q^{17} +(-1.00000 - 2.00000i) q^{20} -2.00000i q^{23} +(-3.00000 + 4.00000i) q^{25} -4.00000 q^{26} +2.00000i q^{28} +1.00000 q^{29} +4.00000 q^{31} +5.00000i q^{32} -2.00000 q^{34} +(4.00000 - 2.00000i) q^{35} -2.00000i q^{37} +(6.00000 - 3.00000i) q^{40} -10.0000 q^{41} +2.00000 q^{46} +12.0000i q^{47} +3.00000 q^{49} +(-4.00000 - 3.00000i) q^{50} +4.00000i q^{52} +12.0000i q^{53} -6.00000 q^{56} +1.00000i q^{58} +4.00000 q^{59} +2.00000 q^{61} +4.00000i q^{62} -7.00000 q^{64} +(8.00000 - 4.00000i) q^{65} -2.00000i q^{67} +2.00000i q^{68} +(2.00000 + 4.00000i) q^{70} +8.00000 q^{71} +14.0000i q^{73} +2.00000 q^{74} -8.00000 q^{79} +(1.00000 + 2.00000i) q^{80} -10.0000i q^{82} +6.00000i q^{83} +(4.00000 - 2.00000i) q^{85} +10.0000 q^{89} -8.00000 q^{91} -2.00000i q^{92} -12.0000 q^{94} -10.0000i q^{97} +3.00000i q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 2 q^{4} - 2 q^{5}+O(q^{10})$$ 2 * q + 2 * q^4 - 2 * q^5 $$2 q + 2 q^{4} - 2 q^{5} + 4 q^{10} - 4 q^{14} - 2 q^{16} - 2 q^{20} - 6 q^{25} - 8 q^{26} + 2 q^{29} + 8 q^{31} - 4 q^{34} + 8 q^{35} + 12 q^{40} - 20 q^{41} + 4 q^{46} + 6 q^{49} - 8 q^{50} - 12 q^{56} + 8 q^{59} + 4 q^{61} - 14 q^{64} + 16 q^{65} + 4 q^{70} + 16 q^{71} + 4 q^{74} - 16 q^{79} + 2 q^{80} + 8 q^{85} + 20 q^{89} - 16 q^{91} - 24 q^{94}+O(q^{100})$$ 2 * q + 2 * q^4 - 2 * q^5 + 4 * q^10 - 4 * q^14 - 2 * q^16 - 2 * q^20 - 6 * q^25 - 8 * q^26 + 2 * q^29 + 8 * q^31 - 4 * q^34 + 8 * q^35 + 12 * q^40 - 20 * q^41 + 4 * q^46 + 6 * q^49 - 8 * q^50 - 12 * q^56 + 8 * q^59 + 4 * q^61 - 14 * q^64 + 16 * q^65 + 4 * q^70 + 16 * q^71 + 4 * q^74 - 16 * q^79 + 2 * q^80 + 8 * q^85 + 20 * q^89 - 16 * q^91 - 24 * q^94

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1305\mathbb{Z}\right)^\times$$.

 $$n$$ $$146$$ $$262$$ $$901$$ $$\chi(n)$$ $$1$$ $$-1$$ $$1$$

## 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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000i 0.707107i 0.935414 + 0.353553i $$0.115027\pi$$
−0.935414 + 0.353553i $$0.884973\pi$$
$$3$$ 0 0
$$4$$ 1.00000 0.500000
$$5$$ −1.00000 2.00000i −0.447214 0.894427i
$$6$$ 0 0
$$7$$ 2.00000i 0.755929i 0.925820 + 0.377964i $$0.123376\pi$$
−0.925820 + 0.377964i $$0.876624\pi$$
$$8$$ 3.00000i 1.06066i
$$9$$ 0 0
$$10$$ 2.00000 1.00000i 0.632456 0.316228i
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ 0 0
$$13$$ 4.00000i 1.10940i 0.832050 + 0.554700i $$0.187167\pi$$
−0.832050 + 0.554700i $$0.812833\pi$$
$$14$$ −2.00000 −0.534522
$$15$$ 0 0
$$16$$ −1.00000 −0.250000
$$17$$ 2.00000i 0.485071i 0.970143 + 0.242536i $$0.0779791\pi$$
−0.970143 + 0.242536i $$0.922021\pi$$
$$18$$ 0 0
$$19$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$20$$ −1.00000 2.00000i −0.223607 0.447214i
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 2.00000i 0.417029i −0.978019 0.208514i $$-0.933137\pi$$
0.978019 0.208514i $$-0.0668628\pi$$
$$24$$ 0 0
$$25$$ −3.00000 + 4.00000i −0.600000 + 0.800000i
$$26$$ −4.00000 −0.784465
$$27$$ 0 0
$$28$$ 2.00000i 0.377964i
$$29$$ 1.00000 0.185695
$$30$$ 0 0
$$31$$ 4.00000 0.718421 0.359211 0.933257i $$-0.383046\pi$$
0.359211 + 0.933257i $$0.383046\pi$$
$$32$$ 5.00000i 0.883883i
$$33$$ 0 0
$$34$$ −2.00000 −0.342997
$$35$$ 4.00000 2.00000i 0.676123 0.338062i
$$36$$ 0 0
$$37$$ 2.00000i 0.328798i −0.986394 0.164399i $$-0.947432\pi$$
0.986394 0.164399i $$-0.0525685\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 6.00000 3.00000i 0.948683 0.474342i
$$41$$ −10.0000 −1.56174 −0.780869 0.624695i $$-0.785223\pi$$
−0.780869 + 0.624695i $$0.785223\pi$$
$$42$$ 0 0
$$43$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 2.00000 0.294884
$$47$$ 12.0000i 1.75038i 0.483779 + 0.875190i $$0.339264\pi$$
−0.483779 + 0.875190i $$0.660736\pi$$
$$48$$ 0 0
$$49$$ 3.00000 0.428571
$$50$$ −4.00000 3.00000i −0.565685 0.424264i
$$51$$ 0 0
$$52$$ 4.00000i 0.554700i
$$53$$ 12.0000i 1.64833i 0.566352 + 0.824163i $$0.308354\pi$$
−0.566352 + 0.824163i $$0.691646\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ −6.00000 −0.801784
$$57$$ 0 0
$$58$$ 1.00000i 0.131306i
$$59$$ 4.00000 0.520756 0.260378 0.965507i $$-0.416153\pi$$
0.260378 + 0.965507i $$0.416153\pi$$
$$60$$ 0 0
$$61$$ 2.00000 0.256074 0.128037 0.991769i $$-0.459132\pi$$
0.128037 + 0.991769i $$0.459132\pi$$
$$62$$ 4.00000i 0.508001i
$$63$$ 0 0
$$64$$ −7.00000 −0.875000
$$65$$ 8.00000 4.00000i 0.992278 0.496139i
$$66$$ 0 0
$$67$$ 2.00000i 0.244339i −0.992509 0.122169i $$-0.961015\pi$$
0.992509 0.122169i $$-0.0389851\pi$$
$$68$$ 2.00000i 0.242536i
$$69$$ 0 0
$$70$$ 2.00000 + 4.00000i 0.239046 + 0.478091i
$$71$$ 8.00000 0.949425 0.474713 0.880141i $$-0.342552\pi$$
0.474713 + 0.880141i $$0.342552\pi$$
$$72$$ 0 0
$$73$$ 14.0000i 1.63858i 0.573382 + 0.819288i $$0.305631\pi$$
−0.573382 + 0.819288i $$0.694369\pi$$
$$74$$ 2.00000 0.232495
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −8.00000 −0.900070 −0.450035 0.893011i $$-0.648589\pi$$
−0.450035 + 0.893011i $$0.648589\pi$$
$$80$$ 1.00000 + 2.00000i 0.111803 + 0.223607i
$$81$$ 0 0
$$82$$ 10.0000i 1.10432i
$$83$$ 6.00000i 0.658586i 0.944228 + 0.329293i $$0.106810\pi$$
−0.944228 + 0.329293i $$0.893190\pi$$
$$84$$ 0 0
$$85$$ 4.00000 2.00000i 0.433861 0.216930i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 10.0000 1.06000 0.529999 0.847998i $$-0.322192\pi$$
0.529999 + 0.847998i $$0.322192\pi$$
$$90$$ 0 0
$$91$$ −8.00000 −0.838628
$$92$$ 2.00000i 0.208514i
$$93$$ 0 0
$$94$$ −12.0000 −1.23771
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 10.0000i 1.01535i −0.861550 0.507673i $$-0.830506\pi$$
0.861550 0.507673i $$-0.169494\pi$$
$$98$$ 3.00000i 0.303046i
$$99$$ 0 0
$$100$$ −3.00000 + 4.00000i −0.300000 + 0.400000i
$$101$$ −2.00000 −0.199007 −0.0995037 0.995037i $$-0.531726\pi$$
−0.0995037 + 0.995037i $$0.531726\pi$$
$$102$$ 0 0
$$103$$ 2.00000i 0.197066i −0.995134 0.0985329i $$-0.968585\pi$$
0.995134 0.0985329i $$-0.0314150\pi$$
$$104$$ −12.0000 −1.17670
$$105$$ 0 0
$$106$$ −12.0000 −1.16554
$$107$$ 6.00000i 0.580042i 0.957020 + 0.290021i $$0.0936623\pi$$
−0.957020 + 0.290021i $$0.906338\pi$$
$$108$$ 0 0
$$109$$ 14.0000 1.34096 0.670478 0.741929i $$-0.266089\pi$$
0.670478 + 0.741929i $$0.266089\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 2.00000i 0.188982i
$$113$$ 14.0000i 1.31701i −0.752577 0.658505i $$-0.771189\pi$$
0.752577 0.658505i $$-0.228811\pi$$
$$114$$ 0 0
$$115$$ −4.00000 + 2.00000i −0.373002 + 0.186501i
$$116$$ 1.00000 0.0928477
$$117$$ 0 0
$$118$$ 4.00000i 0.368230i
$$119$$ −4.00000 −0.366679
$$120$$ 0 0
$$121$$ −11.0000 −1.00000
$$122$$ 2.00000i 0.181071i
$$123$$ 0 0
$$124$$ 4.00000 0.359211
$$125$$ 11.0000 + 2.00000i 0.983870 + 0.178885i
$$126$$ 0 0
$$127$$ 12.0000i 1.06483i −0.846484 0.532414i $$-0.821285\pi$$
0.846484 0.532414i $$-0.178715\pi$$
$$128$$ 3.00000i 0.265165i
$$129$$ 0 0
$$130$$ 4.00000 + 8.00000i 0.350823 + 0.701646i
$$131$$ 12.0000 1.04844 0.524222 0.851581i $$-0.324356\pi$$
0.524222 + 0.851581i $$0.324356\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 2.00000 0.172774
$$135$$ 0 0
$$136$$ −6.00000 −0.514496
$$137$$ 14.0000i 1.19610i −0.801459 0.598050i $$-0.795942\pi$$
0.801459 0.598050i $$-0.204058\pi$$
$$138$$ 0 0
$$139$$ 4.00000 0.339276 0.169638 0.985506i $$-0.445740\pi$$
0.169638 + 0.985506i $$0.445740\pi$$
$$140$$ 4.00000 2.00000i 0.338062 0.169031i
$$141$$ 0 0
$$142$$ 8.00000i 0.671345i
$$143$$ 0 0
$$144$$ 0 0
$$145$$ −1.00000 2.00000i −0.0830455 0.166091i
$$146$$ −14.0000 −1.15865
$$147$$ 0 0
$$148$$ 2.00000i 0.164399i
$$149$$ −6.00000 −0.491539 −0.245770 0.969328i $$-0.579041\pi$$
−0.245770 + 0.969328i $$0.579041\pi$$
$$150$$ 0 0
$$151$$ −24.0000 −1.95309 −0.976546 0.215308i $$-0.930924\pi$$
−0.976546 + 0.215308i $$0.930924\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −4.00000 8.00000i −0.321288 0.642575i
$$156$$ 0 0
$$157$$ 22.0000i 1.75579i −0.478852 0.877896i $$-0.658947\pi$$
0.478852 0.877896i $$-0.341053\pi$$
$$158$$ 8.00000i 0.636446i
$$159$$ 0 0
$$160$$ 10.0000 5.00000i 0.790569 0.395285i
$$161$$ 4.00000 0.315244
$$162$$ 0 0
$$163$$ 4.00000i 0.313304i −0.987654 0.156652i $$-0.949930\pi$$
0.987654 0.156652i $$-0.0500701\pi$$
$$164$$ −10.0000 −0.780869
$$165$$ 0 0
$$166$$ −6.00000 −0.465690
$$167$$ 2.00000i 0.154765i 0.997001 + 0.0773823i $$0.0246562\pi$$
−0.997001 + 0.0773823i $$0.975344\pi$$
$$168$$ 0 0
$$169$$ −3.00000 −0.230769
$$170$$ 2.00000 + 4.00000i 0.153393 + 0.306786i
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$174$$ 0 0
$$175$$ −8.00000 6.00000i −0.604743 0.453557i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 10.0000i 0.749532i
$$179$$ −20.0000 −1.49487 −0.747435 0.664335i $$-0.768715\pi$$
−0.747435 + 0.664335i $$0.768715\pi$$
$$180$$ 0 0
$$181$$ 2.00000 0.148659 0.0743294 0.997234i $$-0.476318\pi$$
0.0743294 + 0.997234i $$0.476318\pi$$
$$182$$ 8.00000i 0.592999i
$$183$$ 0 0
$$184$$ 6.00000 0.442326
$$185$$ −4.00000 + 2.00000i −0.294086 + 0.147043i
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 12.0000i 0.875190i
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −12.0000 −0.868290 −0.434145 0.900843i $$-0.642949\pi$$
−0.434145 + 0.900843i $$0.642949\pi$$
$$192$$ 0 0
$$193$$ 6.00000i 0.431889i 0.976406 + 0.215945i $$0.0692831\pi$$
−0.976406 + 0.215945i $$0.930717\pi$$
$$194$$ 10.0000 0.717958
$$195$$ 0 0
$$196$$ 3.00000 0.214286
$$197$$ 8.00000i 0.569976i −0.958531 0.284988i $$-0.908010\pi$$
0.958531 0.284988i $$-0.0919897\pi$$
$$198$$ 0 0
$$199$$ 16.0000 1.13421 0.567105 0.823646i $$-0.308063\pi$$
0.567105 + 0.823646i $$0.308063\pi$$
$$200$$ −12.0000 9.00000i −0.848528 0.636396i
$$201$$ 0 0
$$202$$ 2.00000i 0.140720i
$$203$$ 2.00000i 0.140372i
$$204$$ 0 0
$$205$$ 10.0000 + 20.0000i 0.698430 + 1.39686i
$$206$$ 2.00000 0.139347
$$207$$ 0 0
$$208$$ 4.00000i 0.277350i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ −12.0000 −0.826114 −0.413057 0.910705i $$-0.635539\pi$$
−0.413057 + 0.910705i $$0.635539\pi$$
$$212$$ 12.0000i 0.824163i
$$213$$ 0 0
$$214$$ −6.00000 −0.410152
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 8.00000i 0.543075i
$$218$$ 14.0000i 0.948200i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −8.00000 −0.538138
$$222$$ 0 0
$$223$$ 18.0000i 1.20537i −0.797980 0.602685i $$-0.794098\pi$$
0.797980 0.602685i $$-0.205902\pi$$
$$224$$ −10.0000 −0.668153
$$225$$ 0 0
$$226$$ 14.0000 0.931266
$$227$$ 6.00000i 0.398234i −0.979976 0.199117i $$-0.936193\pi$$
0.979976 0.199117i $$-0.0638074\pi$$
$$228$$ 0 0
$$229$$ 22.0000 1.45380 0.726900 0.686743i $$-0.240960\pi$$
0.726900 + 0.686743i $$0.240960\pi$$
$$230$$ −2.00000 4.00000i −0.131876 0.263752i
$$231$$ 0 0
$$232$$ 3.00000i 0.196960i
$$233$$ 20.0000i 1.31024i −0.755523 0.655122i $$-0.772617\pi$$
0.755523 0.655122i $$-0.227383\pi$$
$$234$$ 0 0
$$235$$ 24.0000 12.0000i 1.56559 0.782794i
$$236$$ 4.00000 0.260378
$$237$$ 0 0
$$238$$ 4.00000i 0.259281i
$$239$$ 24.0000 1.55243 0.776215 0.630468i $$-0.217137\pi$$
0.776215 + 0.630468i $$0.217137\pi$$
$$240$$ 0 0
$$241$$ 30.0000 1.93247 0.966235 0.257663i $$-0.0829523\pi$$
0.966235 + 0.257663i $$0.0829523\pi$$
$$242$$ 11.0000i 0.707107i
$$243$$ 0 0
$$244$$ 2.00000 0.128037
$$245$$ −3.00000 6.00000i −0.191663 0.383326i
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 12.0000i 0.762001i
$$249$$ 0 0
$$250$$ −2.00000 + 11.0000i −0.126491 + 0.695701i
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 12.0000 0.752947
$$255$$ 0 0
$$256$$ −17.0000 −1.06250
$$257$$ 8.00000i 0.499026i 0.968371 + 0.249513i $$0.0802706\pi$$
−0.968371 + 0.249513i $$0.919729\pi$$
$$258$$ 0 0
$$259$$ 4.00000 0.248548
$$260$$ 8.00000 4.00000i 0.496139 0.248069i
$$261$$ 0 0
$$262$$ 12.0000i 0.741362i
$$263$$ 16.0000i 0.986602i −0.869859 0.493301i $$-0.835790\pi$$
0.869859 0.493301i $$-0.164210\pi$$
$$264$$ 0 0
$$265$$ 24.0000 12.0000i 1.47431 0.737154i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 2.00000i 0.122169i
$$269$$ 26.0000 1.58525 0.792624 0.609711i $$-0.208714\pi$$
0.792624 + 0.609711i $$0.208714\pi$$
$$270$$ 0 0
$$271$$ −24.0000 −1.45790 −0.728948 0.684569i $$-0.759990\pi$$
−0.728948 + 0.684569i $$0.759990\pi$$
$$272$$ 2.00000i 0.121268i
$$273$$ 0 0
$$274$$ 14.0000 0.845771
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 8.00000i 0.480673i 0.970690 + 0.240337i $$0.0772579\pi$$
−0.970690 + 0.240337i $$0.922742\pi$$
$$278$$ 4.00000i 0.239904i
$$279$$ 0 0
$$280$$ 6.00000 + 12.0000i 0.358569 + 0.717137i
$$281$$ 6.00000 0.357930 0.178965 0.983855i $$-0.442725\pi$$
0.178965 + 0.983855i $$0.442725\pi$$
$$282$$ 0 0
$$283$$ 10.0000i 0.594438i −0.954809 0.297219i $$-0.903941\pi$$
0.954809 0.297219i $$-0.0960592\pi$$
$$284$$ 8.00000 0.474713
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 20.0000i 1.18056i
$$288$$ 0 0
$$289$$ 13.0000 0.764706
$$290$$ 2.00000 1.00000i 0.117444 0.0587220i
$$291$$ 0 0
$$292$$ 14.0000i 0.819288i
$$293$$ 6.00000i 0.350524i −0.984522 0.175262i $$-0.943923\pi$$
0.984522 0.175262i $$-0.0560772\pi$$
$$294$$ 0 0
$$295$$ −4.00000 8.00000i −0.232889 0.465778i
$$296$$ 6.00000 0.348743
$$297$$ 0 0
$$298$$ 6.00000i 0.347571i
$$299$$ 8.00000 0.462652
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 24.0000i 1.38104i
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −2.00000 4.00000i −0.114520 0.229039i
$$306$$ 0 0
$$307$$ 8.00000i 0.456584i 0.973593 + 0.228292i $$0.0733141\pi$$
−0.973593 + 0.228292i $$0.926686\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 8.00000 4.00000i 0.454369 0.227185i
$$311$$ −8.00000 −0.453638 −0.226819 0.973937i $$-0.572833\pi$$
−0.226819 + 0.973937i $$0.572833\pi$$
$$312$$ 0 0
$$313$$ 28.0000i 1.58265i 0.611393 + 0.791327i $$0.290609\pi$$
−0.611393 + 0.791327i $$0.709391\pi$$
$$314$$ 22.0000 1.24153
$$315$$ 0 0
$$316$$ −8.00000 −0.450035
$$317$$ 6.00000i 0.336994i −0.985702 0.168497i $$-0.946109\pi$$
0.985702 0.168497i $$-0.0538913\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 7.00000 + 14.0000i 0.391312 + 0.782624i
$$321$$ 0 0
$$322$$ 4.00000i 0.222911i
$$323$$ 0 0
$$324$$ 0 0
$$325$$ −16.0000 12.0000i −0.887520 0.665640i
$$326$$ 4.00000 0.221540
$$327$$ 0 0
$$328$$ 30.0000i 1.65647i
$$329$$ −24.0000 −1.32316
$$330$$ 0 0
$$331$$ 8.00000 0.439720 0.219860 0.975531i $$-0.429440\pi$$
0.219860 + 0.975531i $$0.429440\pi$$
$$332$$ 6.00000i 0.329293i
$$333$$ 0 0
$$334$$ −2.00000 −0.109435
$$335$$ −4.00000 + 2.00000i −0.218543 + 0.109272i
$$336$$ 0 0
$$337$$ 2.00000i 0.108947i −0.998515 0.0544735i $$-0.982652\pi$$
0.998515 0.0544735i $$-0.0173480\pi$$
$$338$$ 3.00000i 0.163178i
$$339$$ 0 0
$$340$$ 4.00000 2.00000i 0.216930 0.108465i
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 20.0000i 1.07990i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 6.00000i 0.322097i −0.986947 0.161048i $$-0.948512\pi$$
0.986947 0.161048i $$-0.0514875\pi$$
$$348$$ 0 0
$$349$$ 2.00000 0.107058 0.0535288 0.998566i $$-0.482953\pi$$
0.0535288 + 0.998566i $$0.482953\pi$$
$$350$$ 6.00000 8.00000i 0.320713 0.427618i
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 28.0000i 1.49029i −0.666903 0.745145i $$-0.732380\pi$$
0.666903 0.745145i $$-0.267620\pi$$
$$354$$ 0 0
$$355$$ −8.00000 16.0000i −0.424596 0.849192i
$$356$$ 10.0000 0.529999
$$357$$ 0 0
$$358$$ 20.0000i 1.05703i
$$359$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$360$$ 0 0
$$361$$ −19.0000 −1.00000
$$362$$ 2.00000i 0.105118i
$$363$$ 0 0
$$364$$ −8.00000 −0.419314
$$365$$ 28.0000 14.0000i 1.46559 0.732793i
$$366$$ 0 0
$$367$$ 24.0000i 1.25279i 0.779506 + 0.626395i $$0.215470\pi$$
−0.779506 + 0.626395i $$0.784530\pi$$
$$368$$ 2.00000i 0.104257i
$$369$$ 0 0
$$370$$ −2.00000 4.00000i −0.103975 0.207950i
$$371$$ −24.0000 −1.24602
$$372$$ 0 0
$$373$$ 4.00000i 0.207112i 0.994624 + 0.103556i $$0.0330221\pi$$
−0.994624 + 0.103556i $$0.966978\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ −36.0000 −1.85656
$$377$$ 4.00000i 0.206010i
$$378$$ 0 0
$$379$$ −20.0000 −1.02733 −0.513665 0.857991i $$-0.671713\pi$$
−0.513665 + 0.857991i $$0.671713\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 12.0000i 0.613973i
$$383$$ 18.0000i 0.919757i −0.887982 0.459879i $$-0.847893\pi$$
0.887982 0.459879i $$-0.152107\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ −6.00000 −0.305392
$$387$$ 0 0
$$388$$ 10.0000i 0.507673i
$$389$$ 2.00000 0.101404 0.0507020 0.998714i $$-0.483854\pi$$
0.0507020 + 0.998714i $$0.483854\pi$$
$$390$$ 0 0
$$391$$ 4.00000 0.202289
$$392$$ 9.00000i 0.454569i
$$393$$ 0 0
$$394$$ 8.00000 0.403034
$$395$$ 8.00000 + 16.0000i 0.402524 + 0.805047i
$$396$$ 0 0
$$397$$ 20.0000i 1.00377i −0.864934 0.501886i $$-0.832640\pi$$
0.864934 0.501886i $$-0.167360\pi$$
$$398$$ 16.0000i 0.802008i
$$399$$ 0 0
$$400$$ 3.00000 4.00000i 0.150000 0.200000i
$$401$$ 34.0000 1.69788 0.848939 0.528490i $$-0.177242\pi$$
0.848939 + 0.528490i $$0.177242\pi$$
$$402$$ 0 0
$$403$$ 16.0000i 0.797017i
$$404$$ −2.00000 −0.0995037
$$405$$ 0 0
$$406$$ −2.00000 −0.0992583
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 22.0000 1.08783 0.543915 0.839140i $$-0.316941\pi$$
0.543915 + 0.839140i $$0.316941\pi$$
$$410$$ −20.0000 + 10.0000i −0.987730 + 0.493865i
$$411$$ 0 0
$$412$$ 2.00000i 0.0985329i
$$413$$ 8.00000i 0.393654i
$$414$$ 0 0
$$415$$ 12.0000 6.00000i 0.589057 0.294528i
$$416$$ −20.0000 −0.980581
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 12.0000 0.586238 0.293119 0.956076i $$-0.405307\pi$$
0.293119 + 0.956076i $$0.405307\pi$$
$$420$$ 0 0
$$421$$ −22.0000 −1.07221 −0.536107 0.844150i $$-0.680106\pi$$
−0.536107 + 0.844150i $$0.680106\pi$$
$$422$$ 12.0000i 0.584151i
$$423$$ 0 0
$$424$$ −36.0000 −1.74831
$$425$$ −8.00000 6.00000i −0.388057 0.291043i
$$426$$ 0 0
$$427$$ 4.00000i 0.193574i
$$428$$ 6.00000i 0.290021i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$432$$ 0 0
$$433$$ 14.0000i 0.672797i −0.941720 0.336399i $$-0.890791\pi$$
0.941720 0.336399i $$-0.109209\pi$$
$$434$$ −8.00000 −0.384012
$$435$$ 0 0
$$436$$ 14.0000 0.670478
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 16.0000 0.763638 0.381819 0.924237i $$-0.375298\pi$$
0.381819 + 0.924237i $$0.375298\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 8.00000i 0.380521i
$$443$$ 24.0000i 1.14027i 0.821549 + 0.570137i $$0.193110\pi$$
−0.821549 + 0.570137i $$0.806890\pi$$
$$444$$ 0 0
$$445$$ −10.0000 20.0000i −0.474045 0.948091i
$$446$$ 18.0000 0.852325
$$447$$ 0 0
$$448$$ 14.0000i 0.661438i
$$449$$ −34.0000 −1.60456 −0.802280 0.596948i $$-0.796380\pi$$
−0.802280 + 0.596948i $$0.796380\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 14.0000i 0.658505i
$$453$$ 0 0
$$454$$ 6.00000 0.281594
$$455$$ 8.00000 + 16.0000i 0.375046 + 0.750092i
$$456$$ 0 0
$$457$$ 8.00000i 0.374224i 0.982339 + 0.187112i $$0.0599128\pi$$
−0.982339 + 0.187112i $$0.940087\pi$$
$$458$$ 22.0000i 1.02799i
$$459$$ 0 0
$$460$$ −4.00000 + 2.00000i −0.186501 + 0.0932505i
$$461$$ −26.0000 −1.21094 −0.605470 0.795868i $$-0.707015\pi$$
−0.605470 + 0.795868i $$0.707015\pi$$
$$462$$ 0 0
$$463$$ 30.0000i 1.39422i −0.716965 0.697109i $$-0.754469\pi$$
0.716965 0.697109i $$-0.245531\pi$$
$$464$$ −1.00000 −0.0464238
$$465$$ 0 0
$$466$$ 20.0000 0.926482
$$467$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$468$$ 0 0
$$469$$ 4.00000 0.184703
$$470$$ 12.0000 + 24.0000i 0.553519 + 1.10704i
$$471$$ 0 0
$$472$$ 12.0000i 0.552345i
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ −4.00000 −0.183340
$$477$$ 0 0
$$478$$ 24.0000i 1.09773i
$$479$$ 36.0000 1.64488 0.822441 0.568850i $$-0.192612\pi$$
0.822441 + 0.568850i $$0.192612\pi$$
$$480$$ 0 0
$$481$$ 8.00000 0.364769
$$482$$ 30.0000i 1.36646i
$$483$$ 0 0
$$484$$ −11.0000 −0.500000
$$485$$ −20.0000 + 10.0000i −0.908153 + 0.454077i
$$486$$ 0 0
$$487$$ 14.0000i 0.634401i −0.948359 0.317200i $$-0.897257\pi$$
0.948359 0.317200i $$-0.102743\pi$$
$$488$$ 6.00000i 0.271607i
$$489$$ 0 0
$$490$$ 6.00000 3.00000i 0.271052 0.135526i
$$491$$ 4.00000 0.180517 0.0902587 0.995918i $$-0.471231\pi$$
0.0902587 + 0.995918i $$0.471231\pi$$
$$492$$ 0 0
$$493$$ 2.00000i 0.0900755i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ −4.00000 −0.179605
$$497$$ 16.0000i 0.717698i
$$498$$ 0 0
$$499$$ 4.00000 0.179065 0.0895323 0.995984i $$-0.471463\pi$$
0.0895323 + 0.995984i $$0.471463\pi$$
$$500$$ 11.0000 + 2.00000i 0.491935 + 0.0894427i
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 4.00000i 0.178351i −0.996016 0.0891756i $$-0.971577\pi$$
0.996016 0.0891756i $$-0.0284232\pi$$
$$504$$ 0 0
$$505$$ 2.00000 + 4.00000i 0.0889988 + 0.177998i
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 12.0000i 0.532414i
$$509$$ 26.0000 1.15243 0.576215 0.817298i $$-0.304529\pi$$
0.576215 + 0.817298i $$0.304529\pi$$
$$510$$ 0 0
$$511$$ −28.0000 −1.23865
$$512$$ 11.0000i 0.486136i
$$513$$ 0 0
$$514$$ −8.00000 −0.352865
$$515$$ −4.00000 + 2.00000i −0.176261 + 0.0881305i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 4.00000i 0.175750i
$$519$$ 0 0
$$520$$ 12.0000 + 24.0000i 0.526235 + 1.05247i
$$521$$ −10.0000 −0.438108 −0.219054 0.975713i $$-0.570297\pi$$
−0.219054 + 0.975713i $$0.570297\pi$$
$$522$$ 0 0
$$523$$ 34.0000i 1.48672i 0.668894 + 0.743358i $$0.266768\pi$$
−0.668894 + 0.743358i $$0.733232\pi$$
$$524$$ 12.0000 0.524222
$$525$$ 0 0
$$526$$ 16.0000 0.697633
$$527$$ 8.00000i 0.348485i
$$528$$ 0 0
$$529$$ 19.0000 0.826087
$$530$$ 12.0000 + 24.0000i 0.521247 + 1.04249i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 40.0000i 1.73259i
$$534$$ 0 0
$$535$$ 12.0000 6.00000i 0.518805 0.259403i
$$536$$ 6.00000 0.259161
$$537$$ 0 0
$$538$$ 26.0000i 1.12094i
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −2.00000 −0.0859867 −0.0429934 0.999075i $$-0.513689\pi$$
−0.0429934 + 0.999075i $$0.513689\pi$$
$$542$$ 24.0000i 1.03089i
$$543$$ 0 0
$$544$$ −10.0000 −0.428746
$$545$$ −14.0000 28.0000i −0.599694 1.19939i
$$546$$ 0 0
$$547$$ 46.0000i 1.96682i 0.181402 + 0.983409i $$0.441936\pi$$
−0.181402 + 0.983409i $$0.558064\pi$$
$$548$$ 14.0000i 0.598050i
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 16.0000i 0.680389i
$$554$$ −8.00000 −0.339887
$$555$$ 0 0
$$556$$ 4.00000 0.169638
$$557$$ 20.0000i 0.847427i −0.905796 0.423714i $$-0.860726\pi$$
0.905796 0.423714i $$-0.139274\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ −4.00000 + 2.00000i −0.169031 + 0.0845154i
$$561$$ 0 0
$$562$$ 6.00000i 0.253095i
$$563$$ 28.0000i 1.18006i 0.807382 + 0.590030i $$0.200884\pi$$
−0.807382 + 0.590030i $$0.799116\pi$$
$$564$$ 0 0
$$565$$ −28.0000 + 14.0000i −1.17797 + 0.588984i
$$566$$ 10.0000 0.420331
$$567$$ 0 0
$$568$$ 24.0000i 1.00702i
$$569$$ 14.0000 0.586911 0.293455 0.955973i $$-0.405195\pi$$
0.293455 + 0.955973i $$0.405195\pi$$
$$570$$ 0 0
$$571$$ 4.00000 0.167395 0.0836974 0.996491i $$-0.473327\pi$$
0.0836974 + 0.996491i $$0.473327\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 20.0000 0.834784
$$575$$ 8.00000 + 6.00000i 0.333623 + 0.250217i
$$576$$ 0 0
$$577$$ 6.00000i 0.249783i −0.992170 0.124892i $$-0.960142\pi$$
0.992170 0.124892i $$-0.0398583\pi$$
$$578$$ 13.0000i 0.540729i
$$579$$ 0 0
$$580$$ −1.00000 2.00000i −0.0415227 0.0830455i
$$581$$ −12.0000 −0.497844
$$582$$ 0 0
$$583$$ 0 0
$$584$$ −42.0000 −1.73797
$$585$$ 0 0
$$586$$ 6.00000 0.247858
$$587$$ 42.0000i 1.73353i 0.498721 + 0.866763i $$0.333803\pi$$
−0.498721 + 0.866763i $$0.666197\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 8.00000 4.00000i 0.329355 0.164677i
$$591$$ 0 0
$$592$$ 2.00000i 0.0821995i
$$593$$ 36.0000i 1.47834i −0.673517 0.739171i $$-0.735217\pi$$
0.673517 0.739171i $$-0.264783\pi$$
$$594$$ 0 0
$$595$$ 4.00000 + 8.00000i 0.163984 + 0.327968i
$$596$$ −6.00000 −0.245770
$$597$$ 0 0
$$598$$ 8.00000i 0.327144i
$$599$$ −36.0000 −1.47092 −0.735460 0.677568i $$-0.763034\pi$$
−0.735460 + 0.677568i $$0.763034\pi$$
$$600$$ 0 0
$$601$$ −2.00000 −0.0815817 −0.0407909 0.999168i $$-0.512988\pi$$
−0.0407909 + 0.999168i $$0.512988\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ −24.0000 −0.976546
$$605$$ 11.0000 + 22.0000i 0.447214 + 0.894427i
$$606$$ 0 0
$$607$$ 28.0000i 1.13648i 0.822861 + 0.568242i $$0.192376\pi$$
−0.822861 + 0.568242i $$0.807624\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 4.00000 2.00000i 0.161955 0.0809776i
$$611$$ −48.0000 −1.94187
$$612$$ 0 0
$$613$$ 40.0000i 1.61558i 0.589467 + 0.807792i $$0.299338\pi$$
−0.589467 + 0.807792i $$0.700662\pi$$
$$614$$ −8.00000 −0.322854
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 18.0000i 0.724653i 0.932051 + 0.362326i $$0.118017\pi$$
−0.932051 + 0.362326i $$0.881983\pi$$
$$618$$ 0 0
$$619$$ −36.0000 −1.44696 −0.723481 0.690344i $$-0.757459\pi$$
−0.723481 + 0.690344i $$0.757459\pi$$
$$620$$ −4.00000 8.00000i −0.160644 0.321288i
$$621$$ 0 0
$$622$$ 8.00000i 0.320771i
$$623$$ 20.0000i 0.801283i
$$624$$ 0 0
$$625$$ −7.00000 24.0000i −0.280000 0.960000i
$$626$$ −28.0000 −1.11911
$$627$$ 0 0
$$628$$ 22.0000i 0.877896i
$$629$$ 4.00000 0.159490
$$630$$ 0 0
$$631$$ −8.00000 −0.318475 −0.159237 0.987240i $$-0.550904\pi$$
−0.159237 + 0.987240i $$0.550904\pi$$
$$632$$ 24.0000i 0.954669i
$$633$$ 0 0
$$634$$ 6.00000 0.238290
$$635$$ −24.0000 + 12.0000i −0.952411 + 0.476205i
$$636$$ 0 0
$$637$$ 12.0000i 0.475457i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 6.00000 3.00000i 0.237171 0.118585i
$$641$$ −50.0000 −1.97488 −0.987441 0.157991i $$-0.949498\pi$$
−0.987441 + 0.157991i $$0.949498\pi$$
$$642$$ 0 0
$$643$$ 10.0000i 0.394362i −0.980367 0.197181i $$-0.936821\pi$$
0.980367 0.197181i $$-0.0631786\pi$$
$$644$$ 4.00000 0.157622
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 18.0000i 0.707653i −0.935311 0.353827i $$-0.884880\pi$$
0.935311 0.353827i $$-0.115120\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 12.0000 16.0000i 0.470679 0.627572i
$$651$$ 0 0
$$652$$ 4.00000i 0.156652i
$$653$$ 6.00000i 0.234798i 0.993085 + 0.117399i $$0.0374557\pi$$
−0.993085 + 0.117399i $$0.962544\pi$$
$$654$$ 0 0
$$655$$ −12.0000 24.0000i −0.468879 0.937758i
$$656$$ 10.0000 0.390434
$$657$$ 0 0
$$658$$ 24.0000i 0.935617i
$$659$$ 28.0000 1.09073 0.545363 0.838200i $$-0.316392\pi$$
0.545363 + 0.838200i $$0.316392\pi$$
$$660$$ 0 0
$$661$$ 26.0000 1.01128 0.505641 0.862744i $$-0.331256\pi$$
0.505641 + 0.862744i $$0.331256\pi$$
$$662$$ 8.00000i 0.310929i
$$663$$ 0 0
$$664$$ −18.0000 −0.698535
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 2.00000i 0.0774403i
$$668$$ 2.00000i 0.0773823i
$$669$$ 0 0
$$670$$ −2.00000 4.00000i −0.0772667 0.154533i
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 12.0000i 0.462566i −0.972887 0.231283i $$-0.925708\pi$$
0.972887 0.231283i $$-0.0742923\pi$$
$$674$$ 2.00000 0.0770371
$$675$$ 0 0
$$676$$ −3.00000 −0.115385
$$677$$ 14.0000i 0.538064i 0.963131 + 0.269032i $$0.0867037\pi$$
−0.963131 + 0.269032i $$0.913296\pi$$
$$678$$ 0 0
$$679$$ 20.0000 0.767530
$$680$$ 6.00000 + 12.0000i 0.230089 + 0.460179i
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 18.0000i 0.688751i 0.938832 + 0.344375i $$0.111909\pi$$
−0.938832 + 0.344375i $$0.888091\pi$$
$$684$$ 0 0
$$685$$ −28.0000 + 14.0000i −1.06983 + 0.534913i
$$686$$ −20.0000 −0.763604
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −48.0000 −1.82865
$$690$$ 0 0
$$691$$ −44.0000 −1.67384 −0.836919 0.547326i $$-0.815646\pi$$
−0.836919 + 0.547326i $$0.815646\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 6.00000 0.227757
$$695$$ −4.00000 8.00000i −0.151729 0.303457i
$$696$$ 0 0
$$697$$ 20.0000i 0.757554i
$$698$$ 2.00000i 0.0757011i
$$699$$ 0 0
$$700$$ −8.00000 6.00000i −0.302372 0.226779i
$$701$$ 30.0000 1.13308 0.566542 0.824033i $$-0.308281\pi$$
0.566542 + 0.824033i $$0.308281\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 28.0000 1.05379
$$707$$ 4.00000i 0.150435i
$$708$$ 0 0
$$709$$ 6.00000 0.225335 0.112667 0.993633i $$-0.464061\pi$$
0.112667 + 0.993633i $$0.464061\pi$$
$$710$$ 16.0000 8.00000i 0.600469 0.300235i
$$711$$ 0 0
$$712$$ 30.0000i 1.12430i
$$713$$ 8.00000i 0.299602i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −20.0000 −0.747435
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$720$$ 0 0
$$721$$ 4.00000 0.148968
$$722$$ 19.0000i 0.707107i
$$723$$ 0 0
$$724$$ 2.00000 0.0743294
$$725$$ −3.00000 + 4.00000i −0.111417 + 0.148556i
$$726$$ 0 0
$$727$$ 40.0000i 1.48352i 0.670667 + 0.741759i $$0.266008\pi$$
−0.670667 + 0.741759i $$0.733992\pi$$
$$728$$ 24.0000i 0.889499i
$$729$$ 0 0
$$730$$ 14.0000 + 28.0000i 0.518163 + 1.03633i
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 50.0000i 1.84679i −0.383849 0.923396i $$-0.625402\pi$$
0.383849 0.923396i $$-0.374598\pi$$
$$734$$ −24.0000 −0.885856
$$735$$ 0 0
$$736$$ 10.0000 0.368605
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 40.0000 1.47142 0.735712 0.677295i $$-0.236848\pi$$
0.735712 + 0.677295i $$0.236848\pi$$
$$740$$ −4.00000 + 2.00000i −0.147043 + 0.0735215i
$$741$$ 0 0
$$742$$ 24.0000i 0.881068i
$$743$$ 20.0000i 0.733729i −0.930274 0.366864i $$-0.880431\pi$$
0.930274 0.366864i $$-0.119569\pi$$
$$744$$ 0 0
$$745$$ 6.00000 + 12.0000i 0.219823 + 0.439646i
$$746$$ −4.00000 −0.146450
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −12.0000 −0.438470
$$750$$ 0 0
$$751$$ −20.0000 −0.729810 −0.364905 0.931045i $$-0.618899\pi$$
−0.364905 + 0.931045i $$0.618899\pi$$
$$752$$ 12.0000i 0.437595i
$$753$$ 0 0
$$754$$ −4.00000 −0.145671
$$755$$ 24.0000 + 48.0000i 0.873449 + 1.74690i
$$756$$ 0 0
$$757$$ 42.0000i 1.52652i −0.646094 0.763258i $$-0.723599\pi$$
0.646094 0.763258i $$-0.276401\pi$$
$$758$$ 20.0000i 0.726433i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 42.0000 1.52250 0.761249 0.648459i $$-0.224586\pi$$
0.761249 + 0.648459i $$0.224586\pi$$
$$762$$ 0 0
$$763$$ 28.0000i 1.01367i
$$764$$ −12.0000 −0.434145
$$765$$ 0 0
$$766$$ 18.0000 0.650366
$$767$$ 16.0000i 0.577727i
$$768$$ 0 0
$$769$$ −38.0000 −1.37032 −0.685158 0.728395i $$-0.740267\pi$$
−0.685158 + 0.728395i $$0.740267\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 6.00000i 0.215945i
$$773$$ 30.0000i 1.07903i 0.841978 + 0.539513i $$0.181391\pi$$
−0.841978 + 0.539513i $$0.818609\pi$$
$$774$$ 0 0
$$775$$ −12.0000 + 16.0000i −0.431053 + 0.574737i
$$776$$ 30.0000 1.07694
$$777$$ 0 0
$$778$$ 2.00000i 0.0717035i
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 4.00000i 0.143040i
$$783$$ 0 0
$$784$$ −3.00000 −0.107143
$$785$$ −44.0000 + 22.0000i −1.57043 + 0.785214i
$$786$$ 0 0
$$787$$ 34.0000i 1.21197i 0.795476 + 0.605985i $$0.207221\pi$$
−0.795476 + 0.605985i $$0.792779\pi$$
$$788$$ 8.00000i 0.284988i
$$789$$ 0 0
$$790$$ −16.0000 + 8.00000i −0.569254 + 0.284627i
$$791$$ 28.0000 0.995565
$$792$$ 0 0
$$793$$ 8.00000i 0.284088i
$$794$$ 20.0000 0.709773